Extra point trivia

I'm playing in three (count 'em, three) e-mail games at the moment (that is, e-mail versions of traditional board games). One is a tournament DoA, the other is finishing up just-for-fun DoA, and the third is a "nice game of chess" with NickV.

Extra point trivia: what movie is the "nice game of chess" from?

Don't click on "comments" until you think you've got it, and no fair using the imdb.