According to Wikipedia, "a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments."
Maxwell Smart's relationship with chess is uneven to say the least.
In his first encounter with the game he confuses it with checkers [Episode #13: "Aboard the Orient Express"] but by the following week has learned enough of its rules and history to face off against Agent 52 and even give a brief analysis of the moves afterward [Episode #14: "Weekend Vampire"].
At some point he begins to play regularly with the Chief who always beats him, resulting in him buying a book on the game written by a child prodigy. But the incident at the Regency Club when he was brainwashed into shooting whoever says the word 'checkmate', almost killing the Chief, left him preferring to unwind with Chinese checkers [Episode #22: Smart the Assassin"].
Indeed, the experience appears to have put him off chess permanently since he is never seen playing again [at least in the televised episodes. In one of the comic strip stories, a game between Max and 99 is interrupted by a call from the Chief on a transmitter in one of the pieces].
Interestingly, a chess table can be seen on and off as part of the post-nuptial redecoration of Max and 99's apartment [eg Episode #96: "The Farkas Fracas"]. Whether this means that Max and the Chief have resumed their games, or Max and 99 play, or whether it is purely for decorative purposes, is unknown. Perhaps it was Mr. Bob's idea.
Chess is also one of Admiral Hargrade's hobbies [Episode #59: "A Man Called Smart, Part 2"].