Anti-King Chess is a variant that adds an Anti-King to the standard set of pieces used in FIDE Chess, and replaces the Pawns with Berolina Pawns.
An Anti-King is a King that is in check only when not attacked by opposing pieces. The goal of Anti-King Chess is to checkmate either your opponent's King or Anti-King.
 
Anti-Kings move like Kings, but can only capture friendly pieces. Being a form of King, Anti-Kings may not be captured, only mated. Anti-Kings do not offer check to friendly Kings. Kings do not attack Anti-Kings.
 
There is no castling, but Kings may make an Knight's leap to an empty square for their first move. Anti-Kings also get this move.
 
The primary feature of this game is the dynamic tension between protecting your King and keeping your Anti-King under attack.
 
A longer, more detailed description of Anti-King can be found at http://www.chessvariants.com/diffobjective.dir/anti-king-chess.html.