As Number Six walks through the Village, he witnesses a guardian sphere moving through the streets. As it approaches, everyone moves to the side and freezes in place to avoid attracting its attention. One elderly man, walking with a stick, ignores the guardian sphere and walks past it, as it moves past him without noticing. Interested, Number Six follows the man with the stick as he goes to a lawn that has been set out as a giant chessboard with Villagers as living playing pieces. The man with the stick invites Number Six to join in and one woman, the white Queen, invites him to play as her pawn.
As the players play on a normal-sized board and their pieces are relayed to the Villagers, the new Number Two monitors the game and notes Number Six's involvement. Number Six asks the Queen who the man with the stick is. She doesn't know but passes on the rumours. Number Six talks about escaping and the Queen offers to help him. Distracted, he finally makes the declared move and Number Two is satisfied he's not up to anything. However, the White Rook suddenly moves on his own, stepping forward and putting the Black King in check. Number Two orders his immediate removal and medical guardians remove the Rook from the board, and the Queen assures Number Six that he'll be well taken care of.
White wins the game and the man with the stick congratulates Number Six. As the two of them stroll through the Village, the man with the stick notes that he's too old to escape but he still studies the opposition. He warns that the key is to judge by attitudes, and those who can't distinguish black from white fail to escape. He goes on his way and as Number Six returns home, the Queen follows him through the streets. He finally turns back on her and asks what she wants, and she says she wants to help. He wonders if she's helped others and if so, why she's still there. She admits that no one she's helped has ever escaped. Unimpressed, he refuses to accept her help and goes home.
Later, Number Two invites Number Six to come to the Hospital and watch the Rook's treatment. They watch as the Rook undergoes Pavlovian training: he is dehydrated and then forced to choose the correct water dispenser out of four. If he disobeys the voice telling him which one to choose, he receives an electric shock. He finally drinks from the "correct" water dispenser and Number Two and the doctor are satisfied that he's cured of his individuality. Number Six leaves and tests the man with the stick's proposal. He challenges one Villager who casually dismisses him. Number Six then confronts the Rook, who runs away in terror. Number Six catches up to him and demands to know why he ran. The Rook apologizes, thinking Number Six is a warder. Number Six denies it but the Rook doesn't believe him.
Number Six meets with the Rook later and they watch a chess game, aware that they are under surveillance. Under cover of discussing the game, Number Six explains that he has determined that the warders are subconsciously arrogant while the prisoners are subservient. Number Two is suspicious but the doctor assures him that the Rook is cured, so he discontinues surveillance. Meanwhile, Number Six says that if they can determine whom to trust, they can plan their escape. Number Six takes the Rook with him to challenge a gardener, who arrogantly dismisses him. He then challenges a painter who follows his every demand, and a shopkeeper who reacts with fear.
Number Two notices that Number Six is up to something and has him brought in for testing. The doctor is unable to determine any specific behavioral problems or find the key to Number Six's approach. She takes a new approach: she conditions the Queen to fixate on Number Six. She then equips the Queen with a locket, convincing her that Number Six gave it to her. The locket monitors the Queen's life signs: if they show heightened life signs then they'll know Number Six is trying to escape. The Queen is conditioned to betray Number Six if necessary to save him from himself if he tries to escape.
Once released, the Queen follows Number Six about the Village as he and the Rook try to assemble the equipment they need for their escapes. Number Six takes a buggy and manages to escape her temporarily. He and the Rook steal a surveillance camera, then a telephone, then return to the camera post to steal parts from the repairman's buggy. The Queen finds Number Six again and he gets in with her to ask what she's up to. She clams she's in love with him but he doubts her feelings even when she breaks into tears.
That night, Number Six finds the queen in his flat making hot chocolate for him. He demands to know who put her up to her act but she bursts into tears and he lies to comfort her. She leaves, happy. The next day, Number Six and the Rook meet on the beach in a changing hut. The Rook is assembling a radio but warns they need more components. Number Six goes to look for them and sees the Queen watching him. She accuses him of not loving her and points out the locket she claims he gave her. Puzzled, he examines the locket with his picture inside and realizes it has a tracking device. He borrows it and gives it to the Rook, providing him with the transistor he needs. Number Six then moves through the Village, informing his fellow conspirators through coded chess phrases that they are ready to escape that night.
That night, the conspirators meet at the changing hut and send a mayday over the assembled radio. They make contact with a ship and claim they're on a transoceanic flight that crashed in the sea. The Control Room detects the signal but Number Two tells them to let their own ship deal with it. The Rook paddles out to sea with the radio while Number Six goes with the other escapees to stop the guardians in the bell tower from spotting the boat with their searchlights. After a brief struggle, they subdue the guardians and head for the Green Dome.
Number Two is informed that the searchlight guardians have failed to report in. He leaves to investigate but Number Six and the others intercept him and take him hostage. They hear the signal cut off but Number Six realizes that the Rook couldn't have reached the boat yet. He tells the others to hold Number Two there and goes to the beach to investigate. He finds the raft and the radio on the shore, but no sign of the Rook. He sees the boat out to sea and takes the raft out to investigate. A deckhand brings him aboard and escorts him to the skipper. However, someone else is waiting for Number Six: Number Two, seated in his customary place in the Green Dome. He is broadcasting to the boat by closed circuit TV. Number Two reveals that the Rook is with him. Number Six accuses him of being a warder and the Rook denies it, saying Number Six was the one working to betray them. Number Two explains that Number Six's own arrogance and authoritative nature betrayed him: the Rook believed he was a warder and convinced the others, who freed Number Two. Number Two assures Number Six that all of the "pawns" are unharmed and will be returned to the board. The ship that Number Six is aboard is the Village authorities' ship.
Number Six fights the ship's crew and defeats them. However, a guardian sphere arrives and escorts him and the ship back to shore. As Number Six returns to the Village, in the Green Dome the Butler returns a white pawn back to the chessboard.