I have had the pleasure of spending alot of time working in Africa, and did a short stint working on a Chimp conservation project.
There are a couple of things that I saw there that could explain their strength.
1: If you ever see a Chimps skeleton, next to a human one, you will notice how massively thick the bones are compared to ours. That gives them the ability to attach massive musculature to their joints. Secondly, as someone already said, the length of the limbs gives them huge leverage advantages.
2: I have seen a full grown male chimp that had a medical condition that made all his hair fall out. It was only at this point that I appreciated how much muscle they actually carry. They are absolutely massive beasts, especially in the back (All those chins from birth I guess).
3: As everyone has said, they spend their entire lives doing bodyweight workouts, and for all those arguments you always see on this site about pullups vs pulldowns, I think chimps are living proof that pullups win LOL.
4: They can be hyper aggressive, especially the top ranked males (God alone knows what their Test levels are!!!), but no more than us. They do it to protect their families, push themselves up the social hierarchy etc.
5: To the comment that they don't know Ju Jitsu. They don't need to. The ape would tear 99% percent of men to bits in a matter of seconds. He dos'nt know the rules about not biting, gouging, or tearing limbs off.
Any man that could stand up to a chimp would be tough as hell, but would be destroyed by a mountain Gorilla (I have seen one of those literally pull a fair sized tree clean out of the ground, just because he could).