The USS Hood intercepts the Enterprise, bringing new orders and a passenger. Picard is ordered to bring Federation emissary Tam Elbrun to a distant star system outside of Federation territory. Tam is a Betazoid with a history of mental instability, who is a former patient of Deanna Troi, and specializes in first contact situations with new alien life.
Tam has had telepathic abilities from birth, whereas the Betazed norm is to acquire them in adolescence. He is extremely sensitive to the thoughts of others and has difficulty filtering them out. The cumulative stress requires him to seek periodic treatment. He establishes a friendship with Data due to the fact that he cannot receive the android's thoughts, which provides Tam with some respite.
Tam's mission is to establish communication with Tin Man, an alien lifeform that appears to be an organic spaceship. Tin Man is orbiting a star that is about to go supernova, and the Enterprise must convince the alien to leave before the star explodes, and before the Romulans who claim the system as their own, can perform research on it.
Arriving at the star system, the Enterprise encounters a Romulan Warbird. The vessel immediately fires on Enterprise and then moves to destroy Tin Man. Tam sends a telepathic warning to Tin Man, and the organic ship produces an energy wave that destroys the Warbird and damages the Enterprise.
With the star beginning to implode and more Romulans on the way, Picard requests that Tam convince Tin Man to move into Federation space. Having already been in contact from several light years away but not informing the crew, Tam tells Picard what he has learned about the entity to this point. Tin Man, who calls itself Gomtuu, is millennia old, and has come to the star system to die in the supernova. In the past the sentient ship had a crew, which were lost in a radiation accident; Gomtuu, grief-stricken over the loss and aimlessly wandering the galaxy ever since, no longer wishes to live. Tam learns that once there were millions of the ships, and that Gomtuu may have travelled from outside the Milky Way galaxy.
Tam requests that he be beamed aboard Gomtuu so he can better establish contact, but Picard is not certain of this course of action. But, when a second Romulan vessel arrives, Picard decides to send Tam accompanied by Data on an away mission to Gomtuu.
Once aboard, Tam is initially overloaded with information as the ship attempts to relay its life experiences in the space of several seconds. But this soon passes and Tam develops a strong sense of identification with the alien. Tam informs Data that he will stay with Gomtuu, as he only has to deal with the thoughts of one other being and feels that piloting the ship is where he truly belongs.
Suddenly, the organic vessel breaks out of its orbit and sends the Enterprise and the Romulan warbird spinning through space just before the star explodes. Data is returned to the bridge, where he explains that Tam has decided to remain with Gomtuu.
Later, Data discusses Tam's plight with Deanna Troi, and shows an understanding of the emotional attributes of loneliness, and the respective joy that was brought to both Gomtuu and Tam when in each other's company. He realises that the Enterprise is where he belongs.