CHOMP is a two-person game invented by David Gale which can be played with pencil and paper. For the finite version of the game, there is an elegant proof that the first player always has a winning move. Surprisingly, the winning first move is known only in a handful of special cases, and that is nearly all that is known about the game. In this talk I will share what I have learned about the game and then challenge the audience to a game of CHOMP.