Just sayin', this is nearly already the definitive chess program.

All of the following is IMO, so you know.
Sprites could be changed... If greyscale sprites are possible, they'd be great, but if you can't do that, at least change bishops and pawns. They're only two pixels apart, and it can get frustrating sometimes to tell the difference... =)
Also, I personally think the selection cursor should be third-tier greyscale, or flash faster. I've made some mistakes because I can't tell the difference between the selection cursor and the possible-moves boxes. Also, I think an option to not show possible moves should be available as well, since it's just a distraction to some...
The AI also tends to make really bad opening moves. I would recommend programming in a couple simple openings. If nothing else, have it start with king pawn or queen pawn most of the time... The game gets pretty bad when the AI starts by putting a knight on the rim. =D

Overall, absolutely great! My chess buddies'll love this.
Points made:
Greyscale sprites or Change bishops/pawns
Increase cursor flash-rate or make it third-tier greyscale
Make option to not show possible moves
Program in openings, or at least have it start with e4/e5/d4/d5.

Sprites could be changed... If greyscale sprites are possible, they'd be great, but if you can't do that, at least change bishops and pawns. They're only two pixels apart, and it can get frustrating sometimes to tell the difference... =)

I agree that the bishop and pawn sprites are too close together, especially because when you highlight them, they look the same. However, I don't know what to use instead. The problem with grayscale sprites though is that it's hard to see them. The problem is that there aren't really any colors available to make the sprites with. You can't do much work with white and light gray because they are used in the board. Which only leaves dark gray and black, which depending on contrast, can look pretty similar.

Also, I personally think the selection cursor should be third-tier greyscale, or flash faster. I've made some mistakes because I can't tell the difference between the selection cursor and the possible-moves boxes. Also, I think an option to not show possible moves should be available as well, since it's just a distraction to some...

Changing the cursor isn't a bad idea, the question though would be which cursor to change, the current one or the new moves one. I'll make some changes and see which one looks better. I'll also add that option to disable the new move boxes, that's really easy.

The AI also tends to make really bad opening moves. I would recommend programming in a couple simple openings. If nothing else, have it start with king pawn or queen pawn most of the time... The game gets pretty bad when the AI starts by putting a knight on the rim. =D

For now, I'll probably leave the opening moves up to the AI. My goal is to get to the point where it figures out what to do by itself.

•make an option for the cursor to not change position after the AI moves

Ok, that's quite easy to do.

•take care of threefold repetition/50-move rule (if it's not too hard)

Those are the easy stalemates, I can do those with simple counters.

•take care of stalemate

Actually, after thinking about this. If I make a special stalemate routine, as opposed to using the AI routine to check for moves, stalemate detection shouldn't take more than .01 seconds.

•provide the AI with an opening book and endgame database, and make it so that it tries to checkmate, since even when I try to lose, the AI checks me perpetually or stalemates me (even when there is an obvious mate in one)

Again, I'm not going to do this for a while because it would be a heck of a lot easier if the AI can just figure it out.

•odds (show a chess board; the user can click a square to toggle whether he/she starts with that piece in the beginning or not)

So basically you can choose to handicap yourself? I'm not entirely sure what you mean.

That's one I've thought about for a long time. I'll probably add it, but it will definitely be disabled by default.

Awesome! By the way the grayscale looked perfect on my 84+. I'm amazed we now finally have grayscale that looks as great as on 68K calcs or extremly close. Back in 2004-05, most people said this would never be possible.

I really wish I could test this. I only have an 83+ Black Edition.

EDIT: Although I could probably get sweet dough by making and selling professional looking gCn hubs for people with no electronics skills.
Oh, and it would be sweet if this game was compatible with globalCALCnet.

I played against the AI, and after 10 or so moves, after I leave the calculator for about 2 minutes without pushing a button, I try moving the cursor, but the arrow keys stop working (the cursor stops flashing also). I know the program didn't freeze, since the grayscale was still working (not black and white lines). I was forced to pull a battery. I have OS 2.43, but I don't know why this occurs.  

Arrrrg. (Pirate) It got stuck in some endless loop inside the AI. That should not be easy to find so it might be a while before I fix it.

Edit:
   I should make a button to abort the AI.

I was beaten by it for the first time today, but mostly out of stupidity

Sir, you have completed a milestone. This is the first time anyone has actually been checkmated by it, which is a good thing for me


Also, as for updates.
- new move squares are white and dark gray
- option to not move cursor to last AI move
- option to not show possible moves

Currently I'm working on really quick stalemate and checkmate detection. You might notice that the current version takes quite a bit of time to see if you are in checkmate.