Racing King was invented by the Englishman Vernon R. Parton, who invented many different and often popular chess variants. This game was invented in 1961, and is popular (amongst others) in NOST.
Each player has a standard set of pieces without pawns. The opening setup is as below.
King h2; Queen h1; Rook g1, g2; Knight e1, e2; Bishop f1, f2.
King a2; Queen a1; Rook b1, b2; Knight d1, d2; Bishop c1, c2.
In this game, check is entirely forbidden: not only is it forbidden to move ones king into check, but it is also forbidden to check the opponents king. The purpose of the game is to be the first player that moves his king to the eight row. When white moves his king to the eight row, and black moves directly after that also his king to the last row, the game is a draw (this rule is to compensate for the advantage of white that he may move first.)
Apart from the above, pieces move and take precisely as in normal chess.
In 1970, Parton invented a variant of Racing Kings, named Dodo chess by him. It is less popular as Racing Kings.
The only difference between the two games is the set of forces and the opening setup. Players now have only one rook, and no queen.
The opening setup is as follows.
King a1; Rook a2; Knight c1, c2; Bishop b1, b2.
King h1; Rook h2; Knight f1, f2; Bishop g1, g2.
All other rules are as in Racing Kings above.
Information based on New Rules for Classic Games, by R. W. Schmittberger and Pritchard's Encyclopedia of Chess Variants.