Actually, the above examples in which the words are repeated are more specifically antimetaboles. A chiasmus doesn't need to repeat the same words. For example, "By day the frolic, and the dance by night" - Samuel Johnson, "The Vanity of Human Wishes" is a chiasmus, but not an antimetabole.

The definition I know chiasmus by is "Reversal of grammatical structures in successive phrases or clauses (but without the repetition of words)", taken from . If this is wrong, someone please tell me.