The U.S.S. Enterprise receives a message from the Sheliak, who order the crew to remove all humans from the planet Tau Cygna V. According to a Federation treaty, the planet belongs to the alien race, who want to take control of their property and have given the crew four days to evacuate the men and women now living there. If the U.S.S. Enterprise does not complete the task, the Sheliak will kill all of the humans, whom they consider "vermin."
Due to the high level of radiation on Tau Cygna V, which the colonists have adapted to over several generations, Data is the only crew member capable of surviving the mission. After Riker speculates that there should be about a dozen humans there, Picard sends the android down to the planet to commence evacuation procedures. But the matter is complicated by Data's reports that 15,000 colonists are living on Tau Cygna V and Worf's estimate that transporting them off the planet will take several weeks, far longer than the Sheliak ultimatum.
What's worse, Data meets resistance to the evacuation plan from Gosheven, the leader of the colony, who refuses to abandon the planet. While Data tries to change Gosheven's mind, Picard's pleas for additional time from the Sheliak, who stick to every word of their 500,000 word treaty, are flatly refused.
While a stirring speech by Data convinces some colonists to revolt against Gosheven, Picard buys time when he finds a clause in the treaty that allows him to demand third party arbitration of the evacuation dispute. He deliberately chooses a race in hibernation for six months, which forces the Sheliak's hand and they agree to give Picard three weeks to relocate the colonists.