KnifeMissile

I've wanted to post this puzzle for a while now but, first, let's say down some terminology.

A chessboard is what we all think of as a chessboard except that we are not concerned with the colour of the squares and it's dimensions needn't necessarily be 8 x 8. A triominoe is a piece that consists of three chessboard squares connected together in an L shape. Finally, a chessboard is said to be defective if it is missing exactly one square.

Now, prove that every 2^n x 2^n defective chessboard can be tiled with triominoes...