Here's a synopsis of that production, apparently taken from an English handout given to English patrons at the theatre:
DAY 1
The Russian chessplayer Anatolij Sergievski leaves his family's suburban apartment in Moscow to depart for the World Chess Championships 1986 (Story of Chess). At the airport, he is greeted by the KGB-man and his advisor Molokov and another few KGB-men (Where I want to be).
In the Italian town Merano they meet the American chessplayer Freddie Trumper and his advisor Florence Vaszi. Freddie causes a scandal in the hotel vestibule when he insults Anatolij. The incident results in a fight between Freddie and Florence who remembers how her father was captured in Hungary when she was small (Autumn '56).
Florence ends up in the hotel's disco and tries to drown her sorrows (Nobody's on Nobody's side).
DAY 2
The Chess tournament is inaugurated with a ceremony performed by the arbiter (The Arbiter). During the first game Freddie loses his temper and leaves the room (Quartet).
In the evening Florence is sitting alone and miserable in the bar. The Russian player Anatolij walks past and makes contact with her. An attraction and excitement arises between them and they leave the hotel together (Someone Else's Story.)
When Molokov discovers that Anatolij has disappeared, panic breaks out in the Soviet camp, the secret police is alerted.
In Moscow, Anatolij's wife Svetlana and their son are discreetly taken from a church by some KGB-men, to be taken to serve as bait for Anatolij in the west.
Anatolij decides to apply for political asylum, and together with Florence he goes to the American consulate. Later a large press conference is organized there due to the recent incident (Mountain Duet).
From the press conference, Freddie gains knowledge of Anatolij's asylum seeking. Anatolij is forced to confront his innermost thoughts regarding the defection (Anthem).
Intermission.
DAY 3
At the hotel room, Freddie accusingly shows the newspaper to Florence which contains pictures of her with the Soviet player. The confrontation ends with her leaving him (Florence Quits / Pity the Child.)
Svetlana and her son arrive at the hotel in Merano accompanied by two KGB-men. Anatolij's feelings and loyalty are tested by Svetlana and KGB (Endgame). Anatolij leaves the hotel.
Alone, Florence realizes what she truly feels (Heaven Help my Heart). At the same time a confused Svetlana goes in search of her husband (Who am I).
In a celbration of spring in Merano, Anatolij and Florence meet and share a short time of happiness in the crowds of the carnival. Suddenly, Freddie appears and there is a big confrontation (The Deal).
In the calm after the fight, Florence and Anatolij confide in each other (You and I).
DAY 4
At a press conference, the judge informs that the games will continue (The Arbiter).
Florence and Svetlana meet by change and a fight over Anatolij ensues (I know him so well).
Plagued by his conscience, Molokov remembers his great love (Forget me if you can). Nevertheless, he still carries out his threat: If Anatolij joins the west, his family will suffer. He must forfeit the game, blame it on his health and claim that he must return to Moscow.
Anatolij makes his choice, loses the game to save his family ("Capablanca" choir). After the game, Anatolij and Florence say their last sad farewells and part (You and I / Story of Chess).
source
-- SDG