I feel like an idiot whenever I read a movie review that uses this term, because I can’t figure out what the hell it means.
Geez, a guy with the name Alan Smithee, ought to know this one.
It refers to an actor, usually Dennis Hopper, who goes over the top in a portrayal of a character.
What, and with a nick like Alan Smithee?
It means overacting.
Doh! Stupid simulpost
Actually, the actor I’ve seen most commonly tagged with this assesment is William Shatner. 
Only if you have never seen Nathan Lane!
In plain English — you mean overacting?
Ha! Watch one of my movies and see if you think I know what overacting means!
Seriously, though, what is the origin of the term? Was there some overwrought portrayer of Richard III who actually started knawing on the set? I knew from the context it had something to do with overacting, but I guess I thought it must have a more specific meaning or referent.
Here is the Random House The Mavens’ Word of the Day entry for chew the scenery.
Tahnks, Tom. I still don’t know exactly where it comes from, but I reckon I know as much as anyone now.
Aside from our esteemed colleague here, the name Alan Smithee is used by Directors Guild of America members who wish to have their names removed from the credits of feature films. It has to have SOME kind of a credit, and that is the name of choice. I’ve no clue why.