Upon discovering the big chess board in Delta Grove, the pieces on the will be randomly arrayed, with green(white) being the color you can play, and orange(black) being controlled by the computer. Winning the game will unlock a nearby room with a few useful items and upgrades. This is probably the most difficult puzzle in the whole game, as it requires actual skill at chess to beat, and the AI doesn't hold any punches.
But for those of us that lack such skills, this proves to be a very frustrating challenge. Fortunately, we plebeians can tap into the same energy the titans of online chess use to top the charts with inhuman win/loss ratios(until they get banned). That's right, we're gonna cheat.

If you couldn't guess already, we're going to use the power of AI to defeat the AI we face in the game, using this bot in particular:

https://www.365chess.com/board_editor.php

Now, you're going to going to clear the board layout on the website and copy the in-game board to it exactly, as you found it. Once you're finished, press play.

In the chess website, select to play as black, and set the computer to level 10. Start the game.

From here, you're simply going to translate 365chess.com's white moves into System Shock, and System Shock's black moves into 365chess.com. That is to say, whatever move white on the website makes, you will make in System Shock. Whatever move black makes in System Shock, that's the move you will make on the website.

The website bot should win handily.