Although no general strategy for Chomp is known, there is one simple technique which will give you the advantage over someone who doesn't know it:
You can ensure a win if you can make a move that leaves the same number of squares in the the top row and left-hand column.
For example, in the following game 'X' has just made the move shown on the left. The winning move is for 'O' to play as shown on the right, leaving a symmetrical position:
Now whatever move 'X' makes, 'O' can play to restore the symmetrical position, ensuring that 'O' will have the last move and win.
Here's another example. 'X' has just played the move on the left. 'O' can ensure a win by playing the move on the right, leaving the same number of squares in the the top row and left-hand column:
The converse of this technique is that you should avoid leaving the game in a position where the other player can make this type of winning move.