"The Other Place" is a pocket-universe created, or discovered, by the Brunnen-G. It is a place where players that are truly dedicated to the pursuit of playing chess may retreat, where even the dead can play.
Games are played upon a mechanical chess-set controlled with an elaborate set of handles and levers, moving pieces that are of personal significance to the players, and able to comment upon and lament the decisions of their player. The surrounding landscape changes in order to reflect the state of the game in support of the player that is currently determined to be winning.
One of the other unusual characteristics of "The Other Place" is that it is capable of absolutely upholding any wager placed upon the outcome of the game. This is seen as Kai perceived to be losing, and parts of Zev and Stan begin to disappear as a result of their lives being Kai's wager in his game.
"The Other Place" is only seen in Lexx 4.18 "The Game" when Kai challenges Prince to a game of chess, the stakes; Zev and Stan's lives in exchange for his own being restored. After a difficult match in which Prince is seen to be clearly winning, Kai is able to capitalise on Prince's over-confidence and immediately exploit a mistake in order to win the game against seemingly impossible odds, thus earning Prince's begrudging acceptance in restoring Kai to life, though he refuses to specify when.