Zoo and acting chimps sometimes were prone to emotional upset and acting-out because of the way that they were caught (IIRC they’re bred now, but that wasn’t the case in the past). Some of them caught in the wild were in their mother’s arms when their mother was shot. They are intelligent enough that an experience like this can seriously weird them out. If Cheeta managed to live without this kind of trouble he was fortunate.
"Several episodes featured a pet female chimp named "Bingo", who was dressed exactly the same as Costello. Bingo was fired from the show after biting Costello."
http://en.wikipedia.org/wiki/The_Abbott_and_Costello_Show