Which unarmed martial art would be most effective against an enraged chimp?

Nuke 'em from orbit.

As others have said, no martial arts is going to do jacksquat against a creature that’s going to go straight for your balls and chew your lips off. I think it would break any human’s spirit way too quickly.

I propose our warrior be some sort of thin-lipped eunuch.

Joe Pesci could take a chimp.