Live chess was a form of chess played in the 52nd century. Unlike an ordinary game of chess, this one was a dangerous and barbaric twist on the original board game, and as a result, illegal. However, it remained popular in the criminal underground as a shady spectator sport that drew in sadistic audiences. The name referred to the fact that the pieces were electrified, with the voltage of each piece increasing each time the piece was moved. Players moved the chess pieces at their own peril, risking electrocution. Though they could use protective gauntlets to protect themselves from electrical shock, once the voltage became too great, not even those would protect them from injury.
The Eleventh Doctor played Gantok in a game of live chess for information about the Silence, as he was their "weakest link". The Doctor eventually cornered Gantok on the chessboard, and the only legal move Gantok had left was to move his queen. However, Gantok had used the chess piece too many times and it was coursing with enough voltage to surpass the limits of his protective gauntlet. Unwilling to be humiliated or risk lethal electrical shock, Gantok bargained with the Doctor to concede in exchange for granting him a favour, though with the fear of retribution from the Silence. The Doctor then surrendered the game by declaring checkmate, greatly upsetting the viewing audience. (TV: The Wedding of River Song)
Behind the scenes
According to The Brilliant Book 2012, a book that contains non-narrative-based information, in an alternate universe where all of history happened at once, Cleopatra and Joseph Stalin played live chess with each other.