It seems unlikely.

Chaucer died in 1400. The Oxford English Dictionary records the first usage of the term "zebra" in English occurs c. 1600 (coming from Italy, and from there possibly Portuguese). Caroline Grigson's Menagerie: the History of Exotic Animals in England only mentions zebras actually in England from 18th century onward.

Two areas where there is room for a modicum of doubt:

First, Chaucer appears to have travelled some in Continental Europe and I don't know the history of exotic animals in Europe. However, considering the state of trade with Africa in the 14th century, and especially the fact that the zebra's natural range is in East and South Africa rather than North and West Africa, I think there's no reason to e suspect that zebras were better known on the continent than in England.

Second, there are a few references to apparent Zebras in classical antiquity. I can only find first page of an article called "Zebras in Greek and Roman Antiquity" by Monika Blaskiewcz, which records that there were a few references to zebras that we can recognize in classical texts. However, we are unaware if zebras had a proper name (lost to us) in Greek and Roman times. To me, it seems unlikely, as the texts we have use other terms to describe them: "a wild ass", "a horse tiger", "a tiger-like horse". It seems that the first wasn't given much special attention at all, but the second term was understood as a type of large tiger, and the later as a striped horse. In her chapter "Zoological Knowledge in Ancient Greece and Rome", Liliane Bodson only references zebras in the classics zebras in the context of of this work of Dio Cassio's Roman History, so it seems likely that this was the primary reference to them and I am not missing a tremendous amount of clear zebra knowledge by only seeing the first page of Blaskiewicz's article.

I'm not a Chaucer expert, but it seems like Chaucer may have only known French and Italian, not Greek and Latin. Gilbert Highet's work is dated, so consensus may have changed, but he writes, "Chaucer was not a very deep or intelligent student of the classics." He then goes into very many clear misunderstandings, which may have come from poor Latin or knowing the texts through vernacular retellings. It seems unlikely that even if he had access to it (which seems doubtful), Chaucer would have been aware of that obscure and opaque reference in Cassius Dio to zebras, or any other even more obscure text.

So no, we can say with a fair amount of confidence that Chaucer probably didn't know what a zebra was.