Sounds like a Mythbusters episode to me!
If the bear is coming at you any faster than a slow walk, you are screwed just because of momentum and such. Once it’s close enough to touch, even if you make the one in a million chainsaw kung fu move that kills it instantaneously, it’s still going to squash you.
Crushed by a bear carcass is not a badass epitaph.
“Sawed him a b’ar when he was only three…”
I have my doubts that you could realistically get a bear near a guy making the kind of racket a running chainsaw makes. 
This thread has made me irrationally afraid of being attacked by a bear.
Oh, good point! Hadn’t really thought of the horrendous noise…
Don’t look behind you…
We can’t let them take away our inherent right to arm bears!
As for the lions vs bears argument, this was answered by QI:
I’ll give the bear 3-1 oods but will also note that the last known grizzly in Colorado was killed by a guy with an arrow…in his hand.
Da Bears!
Is the man Ash Williams?.
If so, the bear is in a lot of trouble.
This seems slightly relevant and given the nature of this thread, it might be of interest to dopers.
It all depends on whether the chainsaw is running and in good working order, and whether it’s full of gas. If the chainsaw isn’t running I’d bet on the bear.
No, no, it’s the right to bear arms - which is probably why this guy is going after a bear with a chainsaw. He has to get those arms from somewhere after all.
No, it depends on how fast he carries the chainsaw.
“Well, Chief, would you believe an electric hedge trimmer?”
Missed it by that much.
This is what you use for a fast chainsaw.
Parallel threads are amusing, aren’t they?
Just as I asserted as a noted authority on the subject (not really), the bear wins almost all of the time. It is an apex predator. It is amazingly agile for its size and wields really remarkably sharp claws and teeth. It also apparently has a significant amount of subcutaneous adipose tissue that may well be pierced by the first (and only) thrust by the chainsaw, but after that, perhaps as quickly as 2 seconds, the human would be incapacitated and then within 10 seconds dispatched.
Don’t mess with bears.