Near Chess is similar to Skirmish Chess by Tony Paletta, in that both start with pieces forward one row, eliminating the initial double move of the pawn.

The purpose of Near Chess differs from Skirmish Chess however, in that its purpose to be one of the fastest ways to introduce people to chess, and the world of chess variants, without being trivial to those who play it still. Near Chess expands upon the pawn simplification of Skirmish Chess, and removes rules from regular chess that aren't needed and also makes it harder for new players to learn. The end result is a
game that can be taught quickly to newbies, and get them playing faster.

The rules to Near Chess can be found here:
http://www.chessvariants.org/index/msdisplay.php?itemid=MSnearchess

Zillions adaptation of the game, and variants of it, is here:
http://www.zillionsofgames.com/cgi-bin/zilligames/submissions.cgi/65274?do=show;id=1577

The game can be played online against other people here:
http://play.chessvariants.org/pbm/play.php?game%3DNear+Chess%26settings%3DJPG-Alfaerie

Zillions adaptation of a group of variants using drops (free piece placement) and a Chess960 random shuffle:
http://www.zillionsofgames.com/cgi-bin/zilligames/submissions.cgi/11300?do=show;id=1580