David,
"Assuming the chimpanzee knew it was in a fight from the git go"
I felt that part (ie: at what point does the chimp realize this) of the equation was an important element in the question and one of the reasons you thought this question worth addressing.
Since you specifically mentioned UFC, let's make this realistic w/ pics. The chimp is announced and walked to the ring by his trainer. The fighter comes down to the ring with his team.
They enter the octagon that looks like this and the door is shut:
One of the UFC ring girls then shows us it is the first round, then the bell rings and fight commences.