"Bobby Fischer Live," a movie featuring Chapa as the U.S. chess champion, is to be filmed in Los Angeles, New York, Russia and Iceland.
"Bobby Fischer is considered to be the greatest chess player of all time," the production company said in a news release Thursday.
The company said Fischer's victory over Soviet champion Boris Spassky in 1972 "was historical in bringing relations between the (United States) and (the Soviet Union) to a more calm and cordial state, as well as elevating chess to a much more mainstream and 'cooler' status."
Fischer won a rematch with Spassky in 1992, in a match played in what was then Yugoslavia, which was under a strict U.N. sanction. After the match, Fischer never returned to the United States.
Chapa's film "Polanski Unauthorized" -- about director Roman Polanski's flight from the United States to avoid trial in an alleged statutory rape case -- is to be released in June by Terra Entertainment worldwide on DVD. It is playing at select theaters in Los Angeles.
Fischer died in January 2008 in Iceland following a long illness. He was 64.