Philidor would be an interesting one, because he was also a prominent musician/composer, and he lived in extremely interesting times in France.
@BradStone, you are right that a movie about Chess would be a complete failure. The point of this thread is, instead, to find an interesting person about whom a succesful drama could be made (who happens to be a chess player). Despite the takeover of violent action films in Hollywood, there is still a decent market for biographical drama films (Recent examples include "La Vie en Rose", "The Diving Bell and the Butterfly", "Bright Star", "The Last Station" etc.)
This is why "Searching For Bobby Fischer" was a relatively succesful movie. Josh Waitzkin's personal and family story was interesting enough that it appealed to non-chess players.
So any movie about a Chess player would have to feature someone whose life story was/is interesting enough to merit a biographical drama with or without their chess play. My nominations are Alekhine (as someone mentioned before, he was involved in both World Wars, the Russian Revolution, and also had severe personal issues including depression, mood swings, alcoholism, and even an alleged suicide attempt, not to mention his many wives and unexplained death), plenty of material there for a film.
The rise of Kasparov during the decline of the Soviet Union would be a very interesting one, although given Kasparov's personality he would want to be intimately involved in it, and likely ruin the film by refusing to grant his permission if he didn't like the script or the way he was portrayed. Maybe it can be made after he dies.
Here's the scene: a disillusioned chess master (Bobby Jim) retreats to the mountains to find himself, quitting the game he loves. A group of Pawnee chess students try to enter a local tourney and are told that only there's only black and white in chess--no red. They protest, and get covered with flour and chocolate syrup (so they can play), when in comes Bobby Jim, who takes off his boots, goes into some kind of rant, does a 20 blindfold blitz simul, and kicks everyone's butt. Whaddaya think?