Greg E.:
Check out the Catechism on divorce (CCC 2382-2386):
http://www.scborromeo.org/ccc/p3s2c2a6.htm
"Divorce is a grave offense against the natural law...Divorce is immoral also because it introduces disorder into the family and into society....It can happen that one of the spouses is the innocent victim of a divorce decreed by civil law; this spouse therefore has not contravened the moral law."

What does a founded hope mean?
Since my wife and her lover, as he impregnated her and was accepted through RCIA, made it very clear to the Catholic Church that they would not abide by any annulment decision that DID NOT result in nullity and both of their two surviving children were baptized, I do wonder.
For those who think the "brother and sister" situation might apply here, it does not because it was my wife who abandoned our valid marriage for her lover(which was clear to the Judicial Vicar in the court of first instance), so she would be being rewarded for her planned and executed adultery. This would seem to really beg the question of justice, as the perpetrator(s) would be rewarded for the crime.
In addition, since I remain faithful to our vows and have, for twenty years been, unsuccessfully, asking the clergy for help to work to heal the valid marriage(and have been ignored and worse) there is no "justification" for my wife remaining with her lover. Usually the circumstances are such that there is no hope for reconciliation with the spouse who did the abandoning(duh?) so the spouse who was abandoned, and found themselves(another joke, found themselves?) a parent in an "irregular"(why is it not called adulterous?) relationship, is in a situation where there is no one to return(as is what is SUPPOSED to happen) to and they are "with child' in another "funtioning"(another joke?) relationship, so...in the absence of scandal(another joke, cannot their other children be scandalized or any one else who is aware of what is going on, and therefore be influenced to say(or do), why should I be faithful when I can find a "younger", "hotter" model and beable to stay with them?), for the "good of the children of adultery" the "brother and sister"(horrendous joke in many situation where it is scandalously applied(with the blessing of countless priests and their bishops)) accomodation is morally justified.
So, just what does constitute a founded hope?
I believe it means that my wife and her lover have a "founded hope" that the stress of my life being destroyed through their cooperation with the civil government and the Catholic Church gives them a "founded hope" that I will die early, while the lovers can still be married in the Catholic Church, and since this is quite OK with all the clergy, including the bishops in jurisdiction, including, apparently the Bishop of Rome, this will. morally, "take care of and wash away" all the evil that has been done by all these co-conspirators.
Sure, their children are being raised Catholic and taught every single day that the father of their sisters is a scumbag who deserves to be treated like a discarded fetus at planned parenthood, with the full blessing of the Catholic Church.
And you people wonder why the Catholic Church is not far behind the decay of the rest of society?
I don't.
My only "founded hope' is that Christ will be merciful. He is my only hope.
My opinion on the Chaput decision?
I am glad I am not him. I don't know what I would have done but I think it is wrong to single out homosexuals. Since I do not agree that avoiding scandal is possible in a society where everything is upside down(read Raymond Burke's Canon 915 treatise) I find it openly, gravely, unjust, and TRULY SCANDALOUS AT LEAST TO ME, that in a situation like I am living, that the children of my wife and her lover would be allowed to attend a Catholic School(they have) but the child(as innocent and precious as the two daughters my wife has with her lover) of homosexual lovers cannot!
I think it makes a mockery of our valid marriage.
My next question is:
If the homosexual lovers, agreed, sincerely, to live as "brother and sister" and there would be no
abandoned spouse to return to, could not they be allowed to send their children to a Catholic School? Would it them be "justified" to still disallow attendance?

Would he refuse these children the sacraments of Baptism?
Dr. Edward Peters wrote on the subject. Quoting an excerpt:
Understandably, canon law does not specify exactly what material needs to be mastered by parents and sponsors prior to presenting their child for Baptism. But a clue as to how much (or how little?) might be required is found, I think, in Canon 868 § 1, n. 2, which states that for the licit baptism of a child there is required (beyond parental consent) a "founded hope that the child will be raised Catholic." Most observers would agree, that it is not much of a juridic requirement, especially when the canon goes on to state that only if such a hope is "altogether lacking" can the baptism be, not denied, but delayed for a time according to diocesan policy.
On the other hand, the "founded hope" requirement is generally considered to be more than sufficient grounds for a pastor to delay a child's baptism because of, say, the parents' irregular marriage situation. Although the child's right to baptism will eventually outweigh the parents' duty to rectify their marital status, resulting in conferral of the sacrament, pastoral evidence is clear that many couples do correctly address their own status in the Church as part of the preparation for their child's baptism.
http://www.ewtn.com/library/CANONLAW/PRECHILD.htm

Would he refuse these children the sacraments of Baptism?
Most likely.
Can. 868 §1. For an infant to be baptized licitly:
...
2/ there must be a founded hope that the infant will be brought up in the Catholic religion; if such hope is altogether lacking, the baptism is to be delayed according to the prescripts of particular law after the parents have been advised about the reason.

By barring the child from re-enrolling, there are a LOT of potential problems being sidestepped here, not just what the child hears in the classroom. Parents are involved in school life and their child's education, moreso (hopefully) at a Catholic school. The kid won't just go to school, then go home to Anna and Eve. There are parent/teacher conferences. PTA meetings. Christmas concerts. School plays. Graduations. Field trips needing chaperons. There is no simple "school life" that can be separated from "private life." There will be ample opportunity for the parent and her sexual partner to make their presence (and thus "relationship") known to and shoved in the face of the entire school.

"I haven't read any other comments..."
Perhaps you should have before commenting.

I haven't read any other comments, but this strikes me as odd. Wouldn't the Catholic Church want the children of lesbian parents in their schools? Obviously the children would most likely not get the gospel from their parents. I don't understand the point of hurting the child by declining them a good education and a chance to hear the gospel because the child's parents are disordered.

Chesterton said, "Morality, like art, consists in drawing the line somewhere."
Thank you, Archbishop Chaput, for drawing that line. Continue to draw those lines, in bold colors, so the world may see the work of art that is Catholic Doctrine.

I agree with Bryan, the Church is losing a "teachable" moment for these children. The children are already enrolled in the school and are effectively being "kicked out" due to to the sin of the parents. What else would the Bishop exclude them from? Are they also to be refused access to CCD or PSR classes? Would he refuse these children the sacraments of Baptism? Communion? Confirmation?

It seems to me that there are many people commenting on this story who haven't read it or know the basic background of the story.
I've read comments here and at several others sites where people keep referring to the "girl". There are TWO children involved. One is in the school Kindergarten and won't be allowed to enter into the 1st Grade. The second is in their Preschool class and won't be allowed to enter the Kindergarten class.

I have a feeling that the parents of this hypothetical Mafia family do everything they can to protect the innocence of their children, and are probably hide what they do for a living. It would be hard to hide the fact that someone has 2 mommies.

Do children from Mafia families understand by example that loan-sharking, prostitution, and murder-for-hire are what put their bread and butter on the table, and, if exposed to the truth that these activities are wrong and sinful, would these children be put in the position of having to choose between their love and loyalty to the Church and their own parents?
No, and no!
But children being raised by two men or two women as their "parents" would be put into such a difficult position. Not fair to the child. Not good for them to hear such information at such a tender age.

Rome will have to step in eventually and draw the lines. Are court civil cases for pain and suffering and money far off?
When young, I went with a friend to pay his rent to his landlord in Bayonne NJ and the landlord and I hit it off in his living room on military-political subjects and his two little daughters interrupted and he was very nice with the way he told them not to. We left and I noted to my friend that he seemed a real nice guy and my friend answered that it was John DiGilio who headed all loansharking for northern NJ (and was later killed by his own Genovese crime family).
I'm sure the daughters went to Catholic school with which Hudson County at that time was saturated.
And Queens NY is similar and more so and I never heard of mafia children being turned away. This is an egg waiting to be cracked by the media and Rome should head off the phenomenon of some dioceses doing one thing and others doing the opposite...if in fact a principle is clearly at issue.
Lesbians in such big city situations and in Italy e.g. could file a civil case for pain and suffering and therefore money... due to known crime families also having children in school and not being rejected and with parents known to all as what they are and who cannot possibly be said to be raising children Catholic by example.

The little girl the lesbian coupled wanted to enroll in the Catholic school was potentially being put in position to receive word that the women she considered her parents were in an intrinsically disordered and sinful relationship.
The schoolchildren are being told that in classes, as they should be, since it is the truth. But kindergarten-age youngsters whose putative parents are living in disordered relationships should not attend those classes, or any classes where they will receive information that may traumatize them.
Traumatizing young children is not what Catholic schools exist for. This dear, innocent child, precious as she is, doesn't belong in a Catholic school - the woefully misguided women raising her have seen to that.
When she is a good deal older - 16 or 18 perhaps, if there is ever a good time to learn that the relationship between your putative parents is fundamentally disordered.
Society has done these children no favor whatsoever in allowing same-sex couples to raise them.

Better phrasing: Who said anyone informed the children of anything? If there was any informing, who did it and what were they told?

Who informed the children of what?

It is not OK - ever! - to inform a young child that the very nature of the relationship between those whom she considers to be her parents is disordered and sinful. Even with the putative parents' knowledge and informed consent, it would be cruel and reprehensible for the school to do that to a young child. Ever!
A nearly grown-up mid- or late-teen youngster would be a different story. Older youngsters - almost young adults - should be able to process this information and cope with it. But not, *not* a little girl like this one. No way. Horrible.
As for "what godly influences will this child have in her life?" if she doesn't attend Catholic school - rather than to expose a child to information likely to traumatize her, this question must be left in the hands of the Good God who created her, who loves her, and who died for her salvation. Would anyone deny that He has it in His power to bring influences into this child's life through channels other than the Catholic school?

The pastor of the school would have the responsibility for explaining the Church's teaching to these "parents". I would not automatically assume that this was not done.

I understand the concerns about the child and the teachers being put in an awkward position, but it still seems to me like an opportunity lost. The bishop could have had a talk with the parents to make it clear that as their child got older and attended this school that topics of sexuality and marriage and such would be coming up in class and that the school would not be compromising its teachings on homosexuality one scintilla. He could clearly tell them, "if you choose to keep your child here, they are eventually going to hear on repeated occasions that homosexual acts are immoral and that marriage is one man and one woman, period. We will not back down from that. If you understand this and can accept that this is what you're signing up for by placing your child with us, and won't be coming back to me to complain about it later, so be it. Your child is welcome. If this is or will become a problem for you, you need to make other arrangements for their education."
I realize the school had the right to do this, I'm just not convinced it was actually the right decision to make. Now what godly influences will this child have in her life? What godly influences will the "parents" have in their life? You had an open door to speak into their lives you've now shut.

"I would assume the same if I ran a legal house of prostitution. Although it may be legal in the eyes of the state, the Church has clear teachings on prostitution."
Exactly correct. And what I think this demonstrates is that the Church must be merciful and forgiving to those who seek to be forgiven and live holy lives, but where people demand the church accommodate their sinfulness, that's quite another matter. I think that perhaps many average parishes have allowed a blind eye to be turned towards certain things for far too long, so that we are now at the point where a topic like this one even comes up.
"The same goes with the attitude of divorce. I may clearly not understand and disagree with the church concerning divorce and be OK (my child could attend the school) - but if I were to open a catering business specifically to help divorced people "celebrate" in their misery - I would assume the Church would have a problem with that."
Indeed it would. But this relates back to the point just above.
In my parish there is a lawyer who is representing a party in a divorce. We well know the church does not approve of divorce, and Pope John Paul II had suggested that Catholic lawyers should not represent parties in divorces. But we see it anyway. And in this instance, the lawyer is not only representing a party in a divorce, but is also divorced and remarried himself. I presume that in this case, there must have been an annulment, which of course I'd accept. Beyond that, however, he is also a Eucharistic minister. Now how, exactly, as I supposed to react to that? And more importantly, if the Church is aware of it (which I doubt) how should it react?

I've been thinking about where the line should be drawn in cases like this one. I read the post you linked to that listed progressively more disordered family situations. While a list like that is instructive, it doesn't give a guideline as to where the line should be drawn. Here's what I am thinking, and I wonder if you agree.
Children whose parents (or "parents") live in open and public defiance of Church law—and, indeed, natural law—regarding marriage should not be admitted to Catholic schools, for the reasons you, Archbishop Chaput, and Fr. Breslin have pointed out.
This would include homosexual couples raising children as if they are a natural family, as well as heterosexual parents cohabitating but not married, because their failure to comply with natural law is public and obvious. Additionally, it would include "polyamorous," er, groups—that is, "families" with more than two adults in the household, involved in a romantic relationship.
It would not include divorced-and-remarried couples (since their annulment status is not public and obvious), couples who are contracepting (again, not a public act), single parents (there are many situations that can lead to single parenting, many of which are not even sins, and others of which are one-time sins that may have been repented and sacramentally forgiven), and parents who disagree with Church teaching (this is not an affront to natural law, and with the grace of God opinions can change over time).
What do others think?

Jimmy, I would like to request that you do a blog entry about divorce. There seems to be a lot of misunderstanding when it comes to this subject.
For example, I have always thought that while the catholic church would encourage a couple to try to work through their issues and stay together, that it understands that divorce does happen. However, the Church does not allow remarriage of divorced people unless it is found that their previous situation was not actually the true state of marriage.
Therefore the fall from grace is not from a divorce, but rather when a divorce person remarries without consulting with the church because it may be possible that the remarried couple are living in a state of adultery.
Could you help clarify?

I think this whole issue has some people concerned about their private life. But marriage is NOT a private issue, it is a public action and that is where the Church clearly defends that marriage is between a man and a woman.
In one of the articles, it was stated that something to the effect that once it was made known what was going on - the diocese and school had no choice but to respond.
I would assume the same if I ran a legal house of prostitution. Although it may be legal in the eyes of the state, the Church has clear teachings on prostitution.
The same goes with the attitude of divorce. I may clearly not understand and disagree with the church concerning divorce and be OK (my child could attend the school) - but if I were to open a catering business specifically to help divorced people "celebrate" in their misery - I would assume the Church would have a problem with that.
And once it is made known, you can't bypass the scandal it would cause to those children. And they have to protect them as much as they can.

I'd rather listen to a Bishop than to a critic.