Well, now that I have time again, I have done a bit of due diligence.
And that quote doesn’t actually exist.
It’s a paraphrase or extended explanation by George Gabriel, from Footnote 28 to an essay called “You Call My Words Immodest” by this same gentleman named George Gabriel, who apparently is some kind of Orthodox or has some interest in Chrysostom. Several Orthodox webpages quote the paraphrase instead of the quote, so it’s not surprising that you would have been given wrong info.
Here is the actual quote from “On Virginity” as he quotes it. (He doesn’t say where it is from, so I’ll search for that next.) I’ll paragraph it a bit more, so that it’s easier to follow the argument:
"Thus, marriage was given to us for procreation also, but much more for the purpose of extinguishing our burning nature. And Paul is a witness to this, saying, `Because of fornications, let each have his own wife,’ and not for the purpose of procreation. And he commands that you come together again, not for you to become fathers of many children.
"But to come together again for what purpose?
So that Satan may not tempt you,’* he says. He continues, but he does not say,come together if you wish children.’
"But what does he say?
"`If they cannot abstain, let them marry.’
"For in the beginning, as it was said, marriage had two purposes. But later, with the earth and the sea and the entire world filled, one reason alone remains: to cast out debauchery and lasciviousness.”
Chrysostom doesn’t say anything about contraception; the text as it stands just says that married couples can come together for other reasons than procreation. It sounds to me like he’s talking about how old married couples or barren married couples can still do it, but I don’t know the context so that’s just my opinion.
Anyway, Footnote 28, which is where your quote comes from, says this:
"The plain meaning of Chrysostom’s words is, ‘If for a certain period, you and your wife have abstained by agreement, perhaps for a time of prayer and fasting, come together again for the sake of your marriage. You do not need procreation as an excuse. It is not the chief reason for marriage. Neither is it necessary to allow for the possibility of conceiving, and thus having a large number of children, something you may not want.’
“He spoke in a manner that was understood perfectly by his audience. In their world, contraception, that is, prevention of conception, and induced abortion were well known for many centuries. Both existed side by side, but the Church condemned abortion and not contraception…”
Gabriel goes on from there for quite a while. (Incorrectly, because there are quite a few patristic texts that object to ancient contraceptive plants like “laser” or other Roman contraceptive devices and sexual techniques.)
It seems odd to me that the actual Chrysostom text would come from “On Virginity” and not from one of his marriage-related works! But I will see whether I can find the passage and what the heck is going on there.
So to sum up: the OP’s quote is actually by George Gabriel, paraphrasing a quote by Chrysostom in an extremely loose way that leaves out most of the actual quote content.