I've seen this quote floating around the internet, attributed to St. Aquinas:

"It would be licit, according to custom, to hold the Jews in perpetual servitude for their crime against Our Lord."

It appears this quote is a misquote inspired by De Regimine Judaeorum, where St. Aquinas writes:

"the Jews by reason of their fault are sentenced to perpetual servitude".

But St. Aquinas is not saying here that Jews should be subjected to chattel slavery, but that Jews who acquire wealth through usury should have their assets stripped from them by the state.

However, I read Wikipedia's Christianity and antisemitism page (and would appreciate a better source if anyone can help) that St. Augustine favored "enslavement of Jews to Catholics". And St. Chrysostom "went so far to say that because Jews rejected the Christian God in human flesh, Christ, they therefore deserved to be killed."

I'd like to think that this is true of St. Augustine and St. Chrysostom.

Do you agree with me that it's a good thing if St. Augustine wanted Jews to be slaves of the Church and St. Chrysostom wanted them killed?

Honestly, with these credentials, I would be reluctant to believe anything this author has to say on the matter. I would like to know where the original quote comes from, if it actually exists.

Editorial Review on "A History of Catholic Antisemitism, the Dark Side of the Church":

Review

"Michael's work is path-breaking, in that few before him have tackled both the historical and theological foundations of Catholic antisemitism and, at the same time, traced its path from biblical times all the way through to Auschwitz. In this, Michael is brave; but, as this outstanding work shows, his bravery is vindicated. His treatment of such topics as the Church’s age-old and ongoing dehumanization of the Jews, coupled with its failure to confront that supreme manifestation of evil that became manifest in the nαzιs, is an important contribution to an already massive literature on antisemitism and the h0Ɩ0cαųst."
--Paul R. Bartrop, Head, Department of History, Bialik College, Melbourne, Australia

About the Author

Robert Michael is Professor Emeritus of European History at the University of Massachusetts, Dartmouth. Listed in Who's Who in America, Professor Michael was a 1997 recipient of the American Historical Association's James Harvey Robinson Prize for the "most outstanding contribution to the teaching and learning of history." A founder of the scholarly e-mail lists H-Antisemitism and H-W-Civ, Dr. Michael has published more than fifty articles and ten books on the history of antisemitism and the h0Ɩ0cαųst.
 

I couldn't find anything on St. Augustine favoring slavery of the Jews.  Had he, it would have not been chattel, I don't think.

As far as St. Chrysostom goes, one finds this, although it'd have to be stretched beyond its pretty clear meaning (he's talking about God-given chastisements of the Jews in the OT) to get to "he favored killing Jews":

(5) But what is the source of this hardness? It come from gluttony and drunkenness. Who say so? Moses himself. "Israel ate and was filled and the darling grew fat and frisky". When brute animals feed from a full manger, they grow plump and become more obstinate and hard to hold in check; they endure neither the yoke, the reins, nor the hand of the charioteer. Just so the Jєωιѕн people were driven by their drunkenness and plumpness to the ultimate evil; they kicked about, they failed to accept the yoke of Christ, nor did they pull the plow of his teaching. Another prophet hinted at this when he said: "Israel is as obstinate as a stubborn heifer". And still another called the Jews "an untamed calf".

(6) Although such beasts are unfit for work, they are fit for killing. And this is what happened to the Jews: while they were making themselves unfit for work, they grew fit for slaughter. This is why Christ said: "But as for these my enemies, who did not want me to be king over them, bring them here and slay them". You Jews should have fasted then, when drunkenness was doing those terrible things to you, when your gluttony was giving birth to your ungodliness-not now. Now your fasting is untimely and an abomination. Who said so? Isaiah himself when he called out in a loud voice: "I did not choose this fast, say the Lord". Why? "You quarrel and squabble when you fast and strike those subject to you with your fists". But if you fasting was an abomination when you were striking your fellow slaves, does it become acceptable now that you have slain your Master? How could that be right? (Against the Jews, "Homily 1", paras. 5-6, link)

The papal bulls Dum Diversas (1452) and Romanus Pontifex (1454) sanctioned slavery of pagan Africans.

It strikes me as odd, if true, that no Churchman has ever been in favor of enslaving Jews, when there are instances of Churchmen in favor of enslavement of far less evil peoples than Jews.

Jesuits in this country owned slaves: https://www.cnn.com/2017/04/18/living/georgetown-slavery-service/index.html

Since Jews are the most evil humans, I would think some notable Churchmen of ages past were in favor of enslaving them.

Pagans aren't nearly as bad as Jews.

Enslaving another human being is evil.

Not according to Catholics of ages past.

I don't buy the argument that slavery is immoral. It's immorality hinges on who is being enslaved. Remember, prisoners with life sentences are slaves and no one bats an eyelash.

Not according to Catholics of ages past.

I don't buy the argument that slavery is immoral. It's immorality hinges on who is being enslaved. Remember, prisoners with life sentences are slaves and no one bats an eyelash.

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Slavery as such isn't immoral, if we understand it merely as the compelled servitude of one toward another.  "Indentured servitude" is really probably a more precise term, distinguishing it from chattel.  I'm not so sure one can find any support for the morality of chattel slavery.
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The two docuмents you referenced are not supportive of chattel.  From what I've been able to find, they are not papally sanctioned raids for a slave trade but rather permissions to enslave those infidels whom the Portuguese were driving from their lands (Both docuмents are letters written to Alfonso V of Portugal from Pope Nicholas V).  Which of course has always been a fairly usual practice among nations, and not one the Church has ever condemned. 
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As far as the Jews go, I think the usual measure taken by princes was simply to expel them or force them to identify themselves.  I'm not so sure slavery would even have occurred to such princes as an especially wise idea, since Jews were known to corrupt Catholics.  Would a Lord really want his Lady waited on by Jews?  When the Jews proved troublesome, as they usually did, segregation-- not servitude-- was the remedy. 

Think of it as me appropriating them into my servitude.