Alice Chess, anyone? I have read about it at British Chess Variants Society, and the work of David Pritchard. It can be accessed at ChessVariants to see about it. Ed Friedlander has a simple PixelPusher program where you can practice it, if the mood strikes.
It plays as standard chess, but two boards are used, and when you make a move on one board, the activated piece moves to the other board.
(hide) If you want to play a game with an opponent of a similar level, you can define a required BKR range for a new game invitation. Then nobody with a BKR outside this range will be able to see/accept it. (Katechka) (show all tips)