Maxim has used a Raspberry Pi to create a chess computer and he’s documented the entire process.
(The game) runs from an Arduino which controls the board, connected to a Raspberry PI which runs the chess engine Stockfish and a chess rules library called Chessboard. It is completely self contained, just plug it in, press the green button and you are playing.
First of all, he helps you to understand the build concepts by getting you to manufacture a noughts-and-crosses (tic-tac-toe) board:
And then gives you the instructions you need to build the full board: