||A normal chess-board is made of 64 squares (8 x 8).|
Since there are only 60 squares in a full set of pentominoes it would not be possible to use them to cover a complete chess-board.
However it is possible to cover a chess-board provided a 'hole' of 4 squares (2 x 2) is left in it.
One example is shown on the right. (The hole is white)
It always possible to find a solution no matter where the hole is placed on the board.