The film flashes back to 1951 Brooklyn, where Fischer's mother, a Soviet Jewish immigrant, explains to 6-year-old Bobby that the FBI has her under surveillance because she supports Marxist revolution in the U.S. She coaches Bobby on what to say to the FBI if he is ever approached.
Bobby immerses himself in chess and becomes an expert player. Despite her worries that chess is becoming an obsession, his mother takes him to an adult chess club, where he impresses the resident chess master and is accepted as a student. Bobby enters the world of professional chess championships and soon becomes the youngest grandmaster ever.
You can watch the whole film on Netflix UK.