Voyager comes across a comet, inside which there is a single living being. It turns out to be a member of the Q Continuum (hereafter designated Quinn, Q is the Q played by John De Lancie). Quinn thanks the Voyager crew for freeing him from his imprisonment, then tries to commit suicide. But he ultimately fails (see omnipotence paradox) and instead of killing himself, he causes all the males on Voyager to vanish.
Q appears and accuses Quinn of sending humans to the Delta Quadrant where they didn't belong yet, then realizes all the men are missing and returns them. Quinn requests Federation asylum from Janeway when Q wants to re-impose the Q Continuum's sentence of imprisonment. Q laughs at the request for asylum but Janeway decides to hold a hearing on Quinn's request. Q reluctantly agrees to make Quinn human if he is granted asylum. He later attempts to bribe Janeway, claiming that if she rules against Quinn, he'll send Voyager home.
During the hearing, Q summons three witnesses to testify that Quinn has been influential in the history of humans, beneficially. Sir Isaac Newton claimed that he was sitting beside Quinn when the apple struck his head (after Quinn stood up to leave, he jostled the tree, causing the apple to fall). Another witness, Maury Ginsberg, claims that if Quinn hadn't offered a ride in his jeep, he would have never made it to Woodstock, got the sound system working and met his future wife. Finally, William T. Riker of the USS Enterprise denies any claim to have known Quinn at all, until Q shows Riker that Quinn had helped his family in the past: As a soldier in the Civil War, Quinn carried a wounded Union officer, Colonel Thaddeus Riker, back from the front lines to safety - ultimately ensuring Will Riker's existence in the future.
Quinn shows the court the Q continuum (or rather how it would be interpreted by their limited human minds) as a road stretching around the entire planet with one rest stop, a country gas station and store, and some Q standing around, bored. Quinn describes immortality as dull, that it is only possible to experience the universe so many times before it gets boring. Q tries to dismiss it and makes a poor attempt to show that the other members of the continuum are happy, but Quinn sees through it and confesses, to Q's surprise, that it was Q's earlier unrestrained behavior in an attempt to make his life fun that was the motivation for his own actions. He makes an impassioned speech comparing his eternal boredom to suffering from a terminal biological disease for which suicide is the only humane release, and that being forced to live for all eternity against his will "cheapens and denigrates" his life, and indeed all life. Janeway is clearly moved by this and agrees to grant him asylum. Keeping his part of the bargain, Q makes him human. At this point Quinn chooses his name.
While trying to decide where to assign Quinn so that he won't use his knowledge to evolve humanity overnight, Janeway and Chakotay receive a message from the Doctor that Quinn is dying after ingesting a poison. After realizing that the Doctor did not keep any of the poison on hand, and that the computer would not replicate it due to its harmful nature, Q then appears and admits that he was the one who gave Quinn the poison. He's taking up Quinn's rebellion against the staid order of the Q.