The Federation starship Enterprise is docked at the Remmler Array to be decontaminated through use of a baryon sweep, harmless to the inorganic materials of the ship but deadly to living beings. The ship is evacuated to the array's base and its systems shut down in preparation for the sweep. Captain Picard and the rest of the senior staff are invited by the Base's Commanding officer, Commander Calvin Hutchinson to a cocktail party, but Picard foresees that he will be cornered by Hutchinson's "small talk" during the event. He returns to the Enterprise to retrieve his riding saddle to go horse riding instead, but on leaving finds an array technician working with the ship's panels. Picard tries to find out what the technician is doing, but he is attacked instead; Picard gains the upper hand and knocks the technician out.
Meanwhile, at the cocktail party, Enterprise Chief Engineer LaForge detects strange readings coming from one of the centerpieces with his VISOR. Before he can investigate, the other array staff members take the partygoers as hostages, injuring LaForge and killing Hutchinson, and prevent them from communicating with the rest of the crew or Starfleet while the sweep is initiated. The crew silently work to devise a plan to break free of their captors.
Aboard the Enterprise, Picard discovers that a small force of technicians, led by a woman named Kelsey, are aboard attempting to steal trilithium resin from the warp engines to sell to another group as part of a powerful explosive. With the baryon sweep progressing through the ship, Picard plays a game of cat-and-mouse with the technicians while staying ahead of the baryon field. At one point, a terrible scream indicates that one of the technicians was caught in the baryon field. Eventually having neutralized all but Kelsey, Picard retreats to Ten-Forward, the last area that will be hit by the sweep. Kelsey manages to beam away to a waiting ship. Picard repeatedly hails the base to deactivate the baryon sweep. The Enterprise officers, having managed to overcome their captors, by an elaborate ruse involving Geordi's visor, are able to stop the sweep just in time to save Picard's life. Data informs Picard of a shuttle trying to escape. Picard, having taken the control rod from the trilithium's storage container during his fight with Kelsey, states that they will not get far as the trilithium explodes destroying the ship.