Chomp can be player on a grid of any size, but square grids or grids with just two rows should be avoided because they have simple winning strategies:
On a square grid the first player wins by taking the largest possible square bite that avoids the poison piece:
From now on the first player simply takes from one edge whatever the opponent takes from the other. Eventually the second player must take the poison piece.
When the grid has two rows the first player can always win by taking the square at bottom right, leaving a pattern in which the top row has one more square than the bottom row:
From now on the first player can always play to restore this situation, ensuring a win.
Apart from these two simple cases, no general strategy for Chomp is known.