After being urged by Counselor Troi and the rest of the crew to take a break, Captain Picard agrees to take a vacation at Risa, a pleasure planet. Just after arriving, Picard is kissed by a woman he has never met.
Picard attempts to relax poolside with a book but is interrupted by Sovak, a Ferengi, and Vash, the woman who kissed Picard upon his arrival. Sovak accuses Picard of conspiring with Vash, who reportedly has stolen a valuable optical disc. Picard has no interest in the quarrel and leaves. As he heads to his room, Vash secretly puts the optical disc Sovak is seeking in Picard's pocket.
When the Captain gets back to his room, he is confronted by two Vorgons who are time travellers from the 27th century and are searching for an object called the Tox Uthat. The Uthat is a powerful weapon, and according to the Vorgons' records, the scientist who invented it travelled back in time to hide the device. The records show that Picard will locate this object on Risa.
The Vorgons leave, and Picard discovers the disc in his pocket. He confronts Vash about it, and she claims the disc was given to her for safekeeping by an archaeologist who had discovered the location of the Uthat. She hid the disc in Picard's pocket to prevent it from falling into Sovak's hands.
With Sovak in pursuit, Picard and Vash use the information on the disc to determine the Uthat's hiding place. They reach some caves and camp for the night. After Vash confesses to Picard that she was paid by Sovak to find the Uthat but double-crossed them, the two discover a deep attraction and give in to passion.
The next morning they set out again. Finally, they arrive at the location where the Uthat is buried. Suddenly, the Vorgons appear, hopeful to intercept the weapon. Also arriving is Sovak. With Sovak holding a gun on them, Vash and Picard excavate the site but do not find the Uthat. The Vorgons vanish, and Vash and Picard return to town.
Early the next day, Vash attempts to sneak away from the resort, but Picard intercepts her. He has realized that Vash already has the Uthat. Her plan all along was to create a ruse that would fool Sovak into thinking the Uthat was lost.
The Vorgons reappear demanding the Uthat, and Vash reveals to Picard that the Vorgons are the people who originally tried to steal the weapon from its inventor in the future. Picard grabs the Uthat and clicks his communicator. The Enterprise is already in orbit, and he orders Riker to use the transporter to destroy it.
The disappointed Vorgons reveal that Picard has acted just as their records said by destroying the Uthat, and they admit defeat and leave. Vash kisses Picard goodbye and heads off on another adventure.