In Budapest, amid the gunfire of the 1956 Hungarian uprising, Gregor Vassy calmly tells his young daughter, Florence, The Story of Chess. As he finishes, Florence is taken away to escape the war-torn country, leaving him behind to fight the Russians.

The sounds of rebellion give way to the furor of a press conference in present-day Bangkok, where the first half of the World Chess Championship is about to be played. The temperamental American chess champion, Freddie Trumper, arrives with Florence, his second, and immediately alienates both the press and his Russian opponents, Anatoly Sergievsky and his second, Ivan Molokov.

Back in his hotel room, Anatoly is told by Molokov that he must play one game with their Ambassador. He ponders who he is, what is expected of him and whether or not it's worth it (Where I Want to Be).

Florence has become increasingly frustrated by Freddie's cheap theatrics and the crass commercialism of his agent, Harper. She asks herself why she should endure such abuse (How Many Women).

Prior to the commencement of the Championship, the Arbiter and the merchandisers sponsoring the event all join in singing the Chess Hymn. During the first game Freddie, accusing Anatoly of cheating, creates a scene and storms out of the arena, leaving Florence, the Arbiter, Molokov and Anatoly to find a way to resume the game (Quartet).

Later, in his hotel room, Freddie berates Florence for cooperating with the Soviets. Warning him that she has had enough, she tells him they are expected to meet with Anatoly and Molokov that night. He will have none of it (You Want to Lose Your Only Friend?) and leaves Florence alone to consider her situation (Someone Else's Story). Shadowed discreetly by Harper, Freddie explores the seamier side of the local nightlife (One Night in Bangkok).