The simple answer to this is “no” — not in the way that cows, goats and sheep do. But the purpose of the question is deeper than this. My negative answer above would appear, at first sight, to be contradictory to what Scripture says, and it is for this reason that the question is much beloved by those who want to undermine belief in the Bible.
And the hare, because he cheweth the cud, but divideth not the hoof; he is unclean unto you. (Leviticus 11:6)
This verse clearly states that the hare (or rabbit in some versions — and these two animals are related and clearly part of the same kind) chews the cud. Yet we know that the rabbit or hare — and I am going to refer to rabbits from now on — is not a ruminant; an animal that chews the cud like cows, sheep and goats. Is the Bible wrong?
No, the Bible is not wrong. The Bible was not written in English. The Old Testament was written in Hebrew. So it is to Hebrew that we should go to understand this conundrum.
The interpretation of the phrase “chewing the cud” depends on the Hebrew words used for chewing and for cud. The Hebrew word for cud is gêrâh. This does not really mean cud, but actually is a broader term, meaning something that has been swallowed. Thus, if your child swallowed a penny, but was able to bring it up again, this could be described as gêrâh — though it would clearly not be what we understood by the English term cud. The Hebrew word that has been translated as chewing is âlâh, which actually means “to ascend” or “to raise.” Therefore, the Hebrew phrase could really be interpreted as “the rabbit raises what it has swallowed … .” Does this broader phrase allow us to classify rabbits with cows, sheep and goats? Yes, it does. Cows, sheep and goats are ruminants. That is to say, they literally chew the cud, in the more narrow sense that the English phrase uses. The key issue is that they are re-eating something. Their first swallowing did not complete the digestion process. Rabbits do something very similar. Rabbits actually produce two different sorts of fecal droppings. First, they produce a light brown dropping. This is actually partially digested food. The rabbits eat these droppings, which is why you might not often notice them. They re-digest these droppings, and then produce their second, darker colored droppings. In this way, the rabbits are raising and re-digesting something which they have already swallowed. Therefore, they fit completely within the terms of the broader Hebrew phrase, even though they cannot be said to “chew the cud” quite like cows do.
So the Bible is correct in its definitions, as always. There are no mistakes in Scripture, even though there can often be misunderstandings.