Are there any animals (e.g., chimps) that can learn to make chess moves?

This is an interesting topic I never researched before.

Yes, in a way (not directly chess but other tasks).  A few years back, this was hot: augmented/enhanced motor control.  For example, your dog can't play chess too easily because it's paws aren't good for picking up pieces and it's muzzle/mouth biting isn't small enough to move single piece without messing up others.  What this field does is to have the dog (say) press a button A, then B, which would move a piece from a4 to a5 (just an off the wall example).  If the buttons are structured well, or if the augmentation only allows certain moves, then the moves can all be legal chess moves.

So animals were doing all kings of silly things.  Finally, the question of whether it is really the animal or the augmentation system that really want the things done came up again.  And the field died.  Now you only find these systems in circus/gov weapons research centers.

cats, that's about it.

What opening would a cat play? The Raw Liver Attack?

i estimate your three legged friend at 10000 (ecf) 75700 (fide) which means that because you've beaten your cat at chess loads of times you're better than stockfish congratulations.

the dracula variation

This thread reminded me of --

Person was playing chess in a park against a dog.  Passerby comments on dog's smartness.  Person replies that the dog isn't smart because it's only won 2 of their 5 games.

The cat in my avatar happens to be a medium-strong Maine Coon cat. 

I think pashak plays from time to time and possibly even that yumyum guy, probably not quite on chimp level but still.

Yes and Pashak has a higher rating than you, stupid duck. 

Lori Marino, a zoologist at Emory University, taught a dolphin to not only play, but in less than 2 years, the dolphin was beating a computer that was programmed to play at a "class D" level. 

"We created an underwater touchscreen computer which the dolphins learned to control using their noses. I had not realized the level of play that one particular dolphin had achieved until we started letting it play against the computer.", noted Dr. Marino.

:from "Dolphins: Smarter Than Your 3-Year Old?"

My guess is that you might be able to teach Checkers or basic Go (my Taiwanese dormmates in college taught me an "easy" version) to a chimpanzee, but chess I don't think is possible.

I remember the high school chess club I coached trying to use a simplified 6x6 chess board and limited number of pieces to play chess in their heads without a board and it was difficult because it was hard to comprehend all the squares each piece controlled, so frequent blunders were made. I would think that the other Great Apes besides us would have a similar problem even if they saw a limited board with limited pieces.

Our ancestors killed-off all the other Great Apes that would challenge us with intelligence: Neanderthal Man, Homo Erectus, etc.  Maybe Dolphins could be taught to do it with an electronic interface.

I taught an ape to play chess once, but he wasn't very good. He didn't comprehend opening principles and insisted on starting with 1b4 as white...

I saw one of those documentaries on Kanzi and he knew how to play Pacman, but chess seems like a stretch.

I know a small elephant who as black plays 1. e4 e5 2. Nf3 d5! We played outdoor.

Yes....me.