From the Maven's Word of the Day at Random House page, written by Carol Braham

Chew (up the) scenery means 'to act melodramatically; overact'. Usually, it's in the context of a play or movie, but it can refer to an aunt of yours who is a frustrated actress. The connotation, either positive or negative, depends on whether the overacting is appropriate to the role or occasion. Here's a recent review from the Topeka Capital-Journal: "Jeff Montague was surely Captain Hook in another life. He minces and chortles, preens and roars and chews the scenery. He is wonderful. It is the best work I have ever seen him do. It is, most likely, the most fun he has ever had on stage --- and it shows." And here's a review of the 1994 film Interview With a Vampire: "While Tom Cruise chews the scenery as the irredeemably evil vampire Lestat, [Brad] Pitt quietly infuses the picture with a powerful melancholy."

I would think it appropriate if a movie mouse, such as Stuart Little or Mickey, chewed the scenery and spit it out. A TV chef could also chew the scenery without apology, especially if he was hamming it up with a glazed ham.

Brewer's Dictionary of Phrase and Fable and a couple of other sources attribute chew the scenery to Dorothy Parker, the writer and humorist. In a 1930 review she wrote: "...more glutton than artist...he commences to chew up the scenery." But Random House Historical Dictionary of American Slang has a much earlier (1894) example from Coeur D'Alene, by Idahoan novelist Mary Hallock Foote. I read a facsimile on the Internet-it first appeared in Century Magazine. The relevant part is about a miner, Jack Darcie, described as being of Scottish family and English education, a young gentleman of prepossessing appearance. After Darcie's entanglements with Faith, daughter of the mining company manager, people gossip about him in a negative light: "Lads, did ye hear him chewin' the scenery, giving' himself away like a play-actor? 'I'm not what ye think I am', says he. 'I'm in a cruel, equizzical position.'...You can't make evidence out of such rot as he was talkin', ...a young fella turning his chin loose about his mash! He chins wid us, an' listens to our talk, but he's too fancy for a miner. He's a bird, he's a swell, and makes out he's a workin'man like the rest av us." (Here "chin" means 'to chat' and "mash," originally theatrical argot, means 'a sweetheart or infatuation.') So Jack Darcie's extravagant and affected character is an example of the negative connotations of 'overacting'.

Extract used with permission