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From Answers.com:
brux·ism (brŭk'sĭz'əm) n.

The habitual, involuntary grinding or clenching of the teeth, usually during sleep, as from anger, tension, fear, or frustration.

Etymology: From New Latin brūxis, a gnashing, from Greek brūkein, to gnash.

The verb is to brux.

Dang, I'll have to gnash my teeth in frustration now, this one's already been suggested. I just read this article on the BBC, http://news.bbc.co.uk/2/hi/uk_news/magazine/8545243.stm and thought it was a good one. Now I'll have to go for its near synonym, gnash. I like them both, though, so perhaps we can have a twofer?

How very incisive! I like it- a word with some dentsity, by gum.

Of course, we've already chewed on this one before...

Ah yes, it looks like I may have bitten off more than I can chew here.

I'll stick with gnash, then. Especially as I was born there, in Bruxville, TN.

Ah yes, it looks like I may have bitten off more than I can chew here.

Some people would give their eye teeth for a remedy for bruxism. Others live with it and eventually give their molars.