You all have been talking about
competitive martial arts. No one has said anything about the variants that are designed to be lethal.
Back in the military, we had a nice sentry-killing move. Basically, you went for a modified chokehold. But instead of going for a choke, you used your forearm to strike the throat (hopefully crushing the trachea, but not necessary), using the momentum of the strike of your forearm to pull the guy backward. Then you lever your shoulder into the base of the skull, and jump backward into a bellyflop. The force of the landing breaks his neck just at the base of the skull. (We actually used this in conjunction with a knife to the kidney, but the knife is clearly verboten in man v. chimp scenario). Properly executed, the sentry's neck pops about a third to half a second from when you first go for the throat strike. There are physiological differences between a chimp and a person that might make this problematic, and this move was designed as a surprise attack, but using some variant of it would likely factor into an optimum lethal attack on a chimp.
Obviously the big problem is getting into position.
I don't know what this ultimate fighting is, and I don't know the capabilities of those fighters, but
in a fight to the death with a chimp my money would be on your average delta trooper/SEAL-type all day long. Maybe even your average Ranger, too, although they tend to be less thoroughly trained in hand to hand combat than the spec ops types mentioned above.
That said, the guy who was my hand to hand combat instructor kills your average chimp in about two and a half seconds, tops.
This sort of fearlessness coupled with the right training in lethal hand to hand combat would be insurmountable for the poor dead chimp.
I believe that your competitive martial artist would first have to train extensively in lethal techniques; having done so, and assuming he had or could develop roughly the same sort of ruthlessness that elite military personnel develop, then there's no reason he couldn't perform at least as well as elite military personnel against the chimp.
By the way, for those of you who have been suggesting that more than one person might stand a better chance against the chimp than would one, I believe this is probably incorrect. Any small group of people, unless they are perfectly trained to work together against a single opponent, are at a marked disadvantage in lethal hand to hand combat against the one person. The single person has the advantages of superior coordination of movement, speed and maneuverability. This may not hold true for a single chimp, though, who may not realize he has those advantages, and therefore might not employ them to best advantage.
For those of you who picked the chimp, I suggest 11 weeks in Ranger school. While there, try to find the instructor who
couldn't take the chimp.