On stardate 41509.1, the USS Enterprise enters the Epsilon Mynos system hoping to find the legendary world of Aldea. The Aldeans, an advanced race devoted to culture and art, are rumored to be able to hide their planet from potential threats. Suddenly, a bright orange planet appears where Data (Brent Spiner) detects a sophisticated, light-refracting shield, a kind of cloaking device. Almost instantly, two Aldeans transport to the bridge - a young woman, Rashella (Brenda Strong), and an older man, Radue (Jerry Hardin). After bidding welcome and offering gifts, they indicate the only way through their shield is "their way". Uncomfortable with the bright light, the Aldeans soon leave. Captain Picard (Patrick Stewart) is delighted to see the myth finally revealed, however Counselor Troi warns that they want something very badly. Commander Riker (Jonathan Frakes), Troi (Marina Sirtis) and Dr. Crusher (Gates McFadden) beam down using the Aldean transporter and meet with Rashella, Radue, and an older woman, Duana (Ivy Bethune). Dr. Crusher observes that the Aldeans do not appear in the best of health.
In space, an energy beam shoots forth from Aldea and enters the Enterprise. It scans everyone on the bridge finally focusing on Wesley Crusher. The beam disappears with Wesley saying it did not hurt him. Reports come in of other scans on all decks, all stopping on the children.
Down on the planet, Radue explains they have revealed themselves because they need a new generation of younger, healthier people to preserve their ways. They have no children and Rashella was the last child born. Dr. Crusher asks what their medical community has done about it, but Rashella indicates that they have tried everything and failed. Radue proposes a trade and asks for some children from the Enterprise. In return they offer knowledge and technology that would take centuries to acquire. Riker flatly refuses, stating that while it might be acceptable to some other race, humans are quite attached to their offspring. Radue is sorry for the rejection and sends the three officers back to the ship.
Beverly returns to the bridge only to see her son Wesley beamed away. Elsewhere on the ship, other children are taken; two boys, Harry and Mason, and four girls, Rose, Tara, Katie and little Alexandra. Radue calls and explains the children are safe and that he would like to discuss "compensation", but Picard demands he return them immediately. Radue suggests talking when the Captain has "calmed down" and signs off. Down on Aldea, the children huddle near Wesley and press him with questions. Rashella, Radue, and Duana tell them they are "guests", but Wesley demands to go home. Radue states the "Custodian" said he would be the leader and it has selected each of them because they are "very special".
Back on the Enterprise, Picard meets with the parents of the abducted children. He promises to do everything in his power to get them back and assures them that the Enterprise will not leave them behind. Later, Data analyzes the Aldean shield and finds a flaw, a weakening of the barrier in certain spots, however the fluctuations are sporadic. Picard asks if it would be possible to beam an away team in through a hole, but Geordi La Forge warns that it would have to be timed perfectly.
Back on the planet, the children are given to families called "units", a group of people with similar talents. Duana explains that Wesley will stay with her and Radue. She takes him to a room and shows him a central console, pointing it out as the "Custodian". Duana explains that the computer provides for their needs and that it was built centuries ago. Wesley asks questions about the machine's specifications, but Duana does not have the answers, stating they have never thought about such things. This seems curious to Wesley, who wonders how the system is maintained. Wesley inquires as to what is behind a huge door in a nearby wall, but Duana does not know, stating it is off limits.
Elsewhere, Picard and Beverly meet with the Aldeans. Picard makes it clear he does not condone their actions. Radue asks why they want the children back so badly and Picard angrily responds that they happen to like these particular children. Rashella promises that the children will have a beautiful life and will be parents to a new breed of Aldeans born of an ancient culture. Angered, Beverly asks what makes them so sure the children will be able to breed since they cannot. Radue assures her that their inability to bear children is a genetic dysfunction and is not contagious. Picard tries to suggest some other solution to their problems, but Radue considers the issue resolved.
After more pressuring, Radue allows Beverly to see Wesley. When she sees him, she secretly hands Wesley the scanner wand from her tricorder. The boy sneaks a scan of Duana and returns the device to his mother. Radue sends Picard and Beverly back to the ship and provides a "small" demonstration of what will happen if they do not accept his deal. He fires an energy beam which sends the Enterprise spiraling away from the planet. They find themselves pushed three days from Aldea at maximum warp. Radue warns that if they do not accept the trade, he will push them so far from Aldea that by the time they get back their children will be grandparents. Days later, the Enterprise returns. Radue welcomes them back, hoping they are now ready to negotiate. With the medical information that Beverly secretly gathered, she indicates that the Aldeans are suffering chromosomal damage, most likely caused by solar radiation poisoning. It is terminal, but reversible if they act now.
On the planet, Wesley gathers the children and explains his plan of passive resistance. If they refuse to do what the Aldean's want they will no longer want to keep them. Rashella enters and wonders why the children are together. They remain silent. She tries to take Alexandra but the girl refuses to cooperate.
Picard calls Radue and indicates he and Dr. Crusher are ready to negotiate. At the moment the two are beamed away, a security team makes transport through an opening in the shield. Picard and Beverly arrive in Radue's office, while Riker and Data materialize in an empty corridor. Radue tells Picard, before they begin, he must talk with the children, explaining they have gone "on strike". Data locates the Custodian room and disables it so it cannot accept further commands. Picard returns with the children, and Radue asks what the problem is. Picard states that they want to go home, but Radue says that is out of the question. Beverly tries to explain the shield has weakened their ozone layer and the planet is being flooded by ultraviolet radiation. They must discontinue use of their shield or they will all die, including the children. Radue refuses to listen, but Picard presses them to understand that the technology they are so dependent on is destroying them. In anger, Radue activates his armband device and tries to send Picard away, but nothing happens.
Picard calls Riker, who acknowledges the disabling of the computer, then prepares to have the children beamed back aboard the ship. Radue curses Picard for destroying their future, but Picard assures him they are doing the opposite. By deactivating the shield, their environment will replenish itself. Picard leads the Aldeans to the sealed room where a massive power core resides. He explains the system is malfunctioning and they must learn how it works if they wish to survive. Radue is finally convinced of their mistakes and welcomes any assistance. Understanding their technological vulnerability, he adds that although the legend will die, the people will live.
Returning to the ship, Picard finds little Alexandra on the bridge; she wanted to give the captain a hug for returning her to her mother. It is clear Picard is nervous around children and is unsure of how to handle them. The girl leaves and Picard orders Geordi to maneuver from orbit. The bridge crew get a laugh as the Captain is unaware of Alexandra's clingy toy which has become stuck to his back.