System Shock

The chess puzzle is located in the Delta Grove, which is attached to Executive. You can't miss it. The green pieces are the white and the red are the black. You're playing white. You may find the board doesn't make any sense when you first get there (for me, the pieces were grouped at the corners and there was 3 of some pieces that should only have 2) so you'll want to quickly lose a game to reset the board. If you're like me and are terrible at chess, you can make use of this website, though it may take a few tries.

Once you win a game, a door in the north corner of the room will open which contains some health patches and most importantly, an inventory upgrade.