Is it legal to keep a chimpanzee as a pet?

I'm curious after watching an episode of Monk yesterday. Someone had a pet chimpanzee, but that was in the US. And obviously Michael Jackson had a pet chimpanzee called Bubbles. Am I right in thinking we have much tighter laws around keeping animals in the UK? Chimpanzees are great though, and would make great pets since they're so intelligent and responsive. However, there was a big news story in the US about a woman who's face was ripped off by a chimpanzee and subsequently became quite a celebrity, telling the media about her ordeal. Not that this should take away from the fact that most chimpanzees are lovely. I suppose it's a bit like dogs, if they're mistreated they can become a problem.