Voyager is holding a party to celebrate "First Contact Day," the day Earth was first openly contacted by an alien civilization (the Vulcans). Included in the celebration is an ancient jukebox playing the favorite music of warp drive pioneer Zefram Cochrane along with his favorite food (cheese pierogi). It has been 315 years since then, thus making this day April 5, 2378.
During the party, the crew of Voyager is surprised to detect a Talaxian settlement hidden within an asteroid belt which is light-years away from the nearest Talaxian territory.
A curious Neelix travels toward the Talaxians' asteroid along with Paris and Tuvok aboard the Delta Flyer, but they are shot down and crash before they can make contact. A company of miners claims the asteroid belt, and they are hostile toward any intruders into their territory.
The Talaxians rescue the Voyager crew and Dexa, a widowed mother, takes a liking to Neelix. The feeling becomes mutual as the two get to know each other. He learns that Dexa's people emigrated to the asteroid and constructed a small city by dismantling the very spacecraft that brought them there. The miners have been pressuring the Talaxians to leave the asteroid which they would like to take for its minerals.
Having been repeatedly driven from one planet to another, the Talaxians would prefer to stay and make the asteroid their permanent home, but have no way to defend themselves against the miners' cooperative and no means for leaving if they wanted to. Neelix being the resourceful person he is, begins to devise a plan for the colony to defend themselves. Using the miners existing shield technology they planned to erect a defensive shield around the asteroid. They must act quickly as not to arouse suspicion. Neelix coordinates the shield placements by using his old shuttle which Voyager has had docked away. Neelix deflects bomb attacks from the miners, loses weapon control and attempts to ram the last mine. The Delta Flyer springs to aid Neelix and helps destroy the bomb. Together they fend off the miners' attacks.
After the miners retreat, Neelix returns to Voyager. He is distressed that he must leave Dexa and her son, Brax and his fellow Talaxians on the asteroid. After a bit of soul-searching, he decides that Voyager will be all right without him, and he joins the Talaxians on the asteroid. Voyager continues toward home, and Captain Janeway bestows on Neelix the title of Official Starfleet Ambassador to the Delta Quadrant.
The crew surprise Neelix with an honor ceremony to mark his departure. The crew of Voyager lines up in the corridors from the turbo lift to the transporter. Tuvok surprises Neelix by doing a small dance step, something the Talaxian had unsuccessfully tried to convince him to do earlier. Neelix, touched by the final gesture, leaves Voyager.