Chimps typically bite the hands off an opponent. They go for the face and eyes, and bite off the fingers of the hands(their fighting is geared toward fighting other primates), because they know the other chimp/human/whatevercan't fight back without fingers. They also know that the genitals of a male are a very vulnerable spot and will use their feet to grab and rib them off. They are very vicious, will hunt and kill other primates for food when in the wild and male chimps will kill their own young and eat them, the females have to protect the young from the males. They have been known to steal children in Africa and eat them also.
If you ever get a chance read some of Jane Goodall's studies on chimps.
I talked to my friend who volunteers in the primate section of the zoo. She says she doesn't have any contact with the animals, which made me wonder exactly what it is she does out there. LOL