As others stated before, this cannot be done in Vanilla Survival MC and needs either mods or command blocks.
Basically create the chessboard somewhere in your world (preferably in the spawn chunks) in it start up state. This is your template board.
Before starting a new chess game, clone the template board to the location of your liking.
Use the same technique to clear the board (create empty template board and clone that).
Example use of clone command:
/clone 100 50 100 108 52 108 ~ ~ ~ /replace
The 6 numbers are two coordinates, each pointing to the cube you want to clone, the three tildes (~) are a coordinate relative to where you stand (so currently the block on the first coordinate of the cube will be cloned to where you stand).
Finding the appropriate coordinates is a bit tricky, so I recommend reading the Wiki entry for it (http://minecraft.gamepedia.com/Commands). There are also plenty of tutorials to be found (for example: https://www.digminecraft.com/game_commands/clone_command.php)