No, he didn't (except for the Second Nun's Tale, the Parson's Tale, and a couple of other things). But I want you to understand his world as well as his words. That world was one in which Boethian and Augustinian ideas laid behind common everyday assumptions even for those people who had never read either one (just as ideas from, say, the Ten Commandments and the Declaration of Independence and the Gettysburg Address underlay our ideas even if we are non-religious and couldn't recite the opening of words of either the Declaration or the Address).
I am not going to claim that Chaucer was an Augustinian (as his contemporary Langland certainly was), but I am going to claim that a few concepts expressed in the City of God are important for understanding some of Chaucer's writing--ideas like man's journey through this world and the importance and operation of the will. Chaucer was a Catholic because the Catholic church was the only church there was (Protestantism is born in the Renaissance). His Catholicism, however, is not the same as modern Catholicism. St. Augustine will help you understand some of the differences
Some of you will take to this reading (philosophy or theology can be extremely interesting as well as challenging reading); others will not. What follows is an attempt to guide you though it. If you like this stuff, simply read the whole thing and ignore my comments. If you find it opaque, read on.
Ch. 1: The two cities are the City of God and the City of Man. Those who live according to the spirit belong to the City of God, etc.
Ch. 2 Skim (which doesn't mean skip).
Ch. 3: Note that Augustine quotes Plato and Virgil. So Chaucer will put quotations from religious and secular sources side by side. Modern readers tend to think of all "religious" people, and especially "religious" people who lived a long time ago as puritanical or as Fundamentalist Christians, but in this chapter and elsewhere you can see that Augustine was no Hawthorne-style Puritan.
Ch. 4: Note that Augustine is no relativist. You know the saying, "if you're not part of the solution, you're part of the problem"? So with Augustine. There is no "secular" middle ground between God and the Devil (though there are surely things that belong to neither, like civil law, yet even there things that belong to God, like honesty and compassion, have a place). Dante exiled those who were neither good nor evil to the outskirts of his Hell in the Divine Comedy; Augustine does not even allow that.
Ch. 5: More evidence that Augustine is no Puritan.
Chs. 6-11: Pay special attention to this emphasis on man's will. Dante, too, points up the importance of the will in man's actions and "destiny." How does this differ from our view of man--or does it?
Ch. 12: Obedience is also a good thing--the sort of thing, though, that we hate and consequently see as wrong or evil. Everybody should do his own thing, right? No authority figures for us!
Ch. 13: Exactly! Adam and Eve wanted to please themselves. Me first. What's wrong with that? Look at the profound consequences of such an attitude!
Keep that phrase "their present pilgrimage on earth" firmly in mind. A pilgrimage is a journey to someplace--where?
Don't we think "love of self" is a good thing? We spend most of our time pleasing ourselves, and our culture tells us that that is what we ought to be doing. What do you think?
Ch. 14: Skim.
Ch. 15: Notice that the effect of pleasing yourself is to become enslaved to yourself. Can you think of instances in the world today? (I mean beyond smoking and drinking.)
Chs. 16-27: Skim. (Notice in passing the interesting idea that, before the Fall of Adam and Eve, sex and the will were congruent [look it up]. That is, whereas we sometime want to have sex and cannot or do not want to have sex and are yet aroused, before the Fall one could will oneself to be aroused sexually; thus you could whenever you wanted to, but never became aroused unless you wanted to be.)
Ch. 28: A summary.