The chess feature is a hidden game that seemingly Facebook didn't announce but was instead discovered on a chess subreddit r/chess last December.
There is of course a chess app for Facebook by the excellent chess.com, which is acclaimed for being an excellent chess site, but this one might just get your buddies playing with you.
There is no point-and-click interface that you might be used to, instead you interact using commands.
Start a new game using @fbchess play.
Get help using @fbchess help.
Use chess notation to make a move. For example: @fbchess Pe4 moves your pawn to e4.
+1 Geek experience point to anyone who finishes a game.