A rhetorical figure in which elements are presented in the order ABBA. It's named for the Greek letter chi (which looks like an "X"). The "X" suggests the crossing that characterizes the figure. Some examples:
This man I thought had been a Lord among wits; but, I find, he is only a wit among Lords.

[On The Beggar's Opera, a fabulously successful play written by John Gay and produced by John Rich:] It made Gay rich and Rich gay.

Ask not what your country can do for you, but what you can do for your country.

We can see the chiasmus in the last example (with "country" and "you") if we lay it out this way (in clumsy ASCII art, but I'm too lazy to work up a graphic):
 Ask not what your country can do for you,
                      \               /
                         \         /
                            \   /
                            /   \
                         /         \
                      /               \
          but what you can do for your country.
Chiasmus doesn't have to be the same words: it's often the same parts of speech in ABBA order. Here's Milton:
Silence, ye troubled Waves, and thou Deep, peace. (PL 7.216)
Notice it's imperative-vocative, vocative-imperative — or, if that's unclear, "Do something, you; you, do something."

A chiasmus can get even more complicated: not only ABBA, but ABCCBA. Consider Genesis 9:6:

Whoever sheds the blood of man, by man shall his blood be shed.
Notice shed-blood-man, man-blood-shed: ABC, CBA.

From the Guide to Literary Terms by Jack Lynch.
Please send comments to Jack Lynch.
Note: This guide is still in the early stages of development.
Three question marks mean I have to write more on the subject. Bear with me.