How is it any different from self-defense against a person? You don't shoot just one time and then stop to look. This ain't a Hollywood movie. You shoot until the threat is obviously stopped. Just like Chairman Jeff always said. The reason for shooting in IDPA or with a stock gun in IPSC is to get your head straight for just this kind of situation. The only difference is the clothing. Chimps ain't got any.
Any law-enforcement handgun oughta suffice. Just don't think in terms of a one-shot kill, is all. Shoot until Bad Chimp quits moving.
If you have the time, sure, a rifle or shotgun is better. That holds true for people as well as chimps. Still, shoot until the problem is resolved. But the average fellow is not carrying a long gun as he walks or jogs past the chimp-lady's house in his evening constitutional.