Some of the flirting that takes place in this 1968 film takes place between the title character (played by Steve McQueen) and an insurance investigator, Vicki Anderson over a game of chess. McQueen's character has masterminded a Boston bank heist, and Anderson, having deduced that he has the money, pursues him for the money and his love. Faye Dunaway, who starred as Anderson, also appeared in the 1999 remake playing a psychologist counseling Pierce Brosnan's title character as he is pursued by Rene Russo's character after stealing a Monet from the Met. Name this film, which replaces the chess with replaces the flirting and chess with overt nudity and sex, and is best remembered for its Oscar winning song "The Windmills of Your Mind".
The Thomas Crown Affair