On Resident Evil 5 how do you defeat the zombie maniac with a chainsaw?

Sure.

With a handgun that is at level one, you are in trouble. Using head shots are the quickest way to take him down aside from using the barrels or any explosives you might have.

Using a sniper rifle for headshots, which you should have at this point, is the next best way.

A rocket launcher or similar weapon is quite effective.

But the point is he is not invincible. He's far from invincible.

Bear in mind that on harder modes, the chainsaw guy is resilient and will get back up if he has been downed once but his chainsaw is still running. He will go into maniac mode. Killing him a second time kills him dead.