I don't think so...
"a fully grown, fit, adult human could likely win a fight against a chimpanzee".
There are lots of ways of measuring strength, so in humans vs. chips, it depends on what you measure.
Fighting is quite another thing and there are lots of ways to fight. But, let's assume the chimp decides how he fights and the human has deal with it. (Chimps don't follow qweenbury rules). Consider that it is biting, clawing and griping your limps to twist them in ways they are not meant to go. I am not sure what the human will do in defense.
With the much superior grip strenght of their hands, once the chimp grabs your arm you are not going to break free. Then he will chomp down on your shoulder or neck with much superior bite strength and teeth to match. Don't think biting back will work.
Hitting him won't work as his head is much stronger. And, finally, he will not feel pain like humans do.
Full grown male chimp vs the best MMA fighter and it will be over within seconds.
I've never seen a chimp fight a man, but I have seen a 30 pound monkey send a man to the emergency room.