After being urged by Counselor Troi and the rest of the crew to take a break, Captain Picard reluctantly agrees to take a vacation at Risa, a pleasure planet which is dedicated to providing tourists with a resort experience. Just after arriving, Picard is kissed by a woman he has never met. After she leaves, saying "Welcome to Risa", he says to himself, "A simple handshake would have sufficed."
Having arrived, Picard attempts to relax poolside, but is constantly interrupted by women coming to ask if he wants company. He tells the fifth one no, she replies that she is confused for he says he wants no company, yet he displays the Horga'hn. The Horga'hn is a souvenir requested by Commander Riker, but the Horga'hn is really a symbol of sexuality and by displaying it, Picard is letting everyone know that he is in search of sexual coupling. After he puts the souvenir away he is rudely interrupted by Sovak, who is a Ferengi, and a human woman named Vash, who was the same woman that kissed Picard. Sovak accuses Picard of conspiring with Vash, who has stolen a valuable optical disc.
Picard has no interest in the quarrel, although he finds the woman intriguing, and leaves. But just as he heads to his room, Vash secretly puts the very optical disc Sovak is seeking in Picard's pocket.
When the Captain gets back to his room he is confronted by two Vorgons, who have been following him. The Vorgons, named Boratus and Ajur, explain that they 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 Vorgon's records, the scientist who invented the Uthat travelled back in time to hide the device. The records also show that Picard will locate this very object on Risa.
The Vorgons leave, and Picard discovers he has 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 failing into Sovak's hands, since the Ferengi had plans to use the disc to find the Uthat and would then proceed to sell it.
With Sovak in pursuit, Picard and Vash use the information on the disc to determine the Uthat's hiding place, and they set out on a search for the weapon. They reach some caves, inside which the Uthat is buried, and camp out for the night. After Vash confesses to Picard that she was actually paid by Sovak to find the Uthat, but that she had double crossed them, the two discover a deep attraction they have for each other. The scene closes with the couple giving 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 unearthing of the weapon. Also arriving is Sovak, who has finally caught up. With Sovak holding a gun at them, Vash and Picard begin excavating the site, but after hours of digging they do not find the Uthat. The Vorgons vanish, and Vash, Picard and Sovak return to town apparently defeated in their search.
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, and had located it long before she met Picard. Her plan all along was to create a ruse that would fool Sovak into thinking the Uthat was lost.
Then, the Vorgons reappear demanding the Uthat, and Vash reveals to Picard that the Vorgons are in fact the people that had originally tried to steal the weapon from its inventor in the future.
Picard grabs the Uthat and clicks his communicator. Unknown to anyone but Picard, the Enterprise is already in orbit, and he orders Riker to use the transporter to destroy it (a "Transporter code 14").
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 she heads off on another adventure.