Here is chess in 1 kb, written in 6502 assembler for the KIM-1 -- in 1976!
http://www.benlo.com/microchess/
The instructions say, "If you are an above average player, you may find that the MICROCHESS program is below your level ..."
Just tried the 2 KB (fast) version as White. Trapped Black's queen on my 7th move.
Mate took 20 moves or so total.
Got stalemated with a bare king against four queens and stuff.
Wow -- that's impressive -- 1kb -- really?
Of course 30 years ago there was "1K Chess" for the Sinclair ZX81 (Timex/Sinclair 1000 for US readers) - which, despite the name, was actually just 672 bytes of code. (The program had to run in a machine with 1K of memory _total_, which obviously included space for the machine's workspace and display file - itself ingeniously optimised to only occupy memory space for parts of the screen that had been printed on.)
https://chessprogramming.wikispaces.com/1K+ZX+Chess