After the Voyager crew is treated to the rare sight of a supernova, Q shows up in Janeway's quarters with a proposition: he'd like the Captain to bear his baby. Janeway flatly refuses, but Q is persistent. He reappears several more times, and although Janeway admits she'd like to have a child someday, she's not going to mate with Q — much to the relief of a jealous female Q who shows up on the ship.
After the crew witnesses the third supernova in as many days, they suspect that Q may be behind the explosions. The shockwaves from the cosmic phenomena could damage Voyager, so Janeway urges Q to do something. In response, Q transports Janeway to the Q Continuum, which now resembles Earth's old antebellum South — an apropos setting, because the Q are in the middle of a civil war.
It all started with the death of Quinn, the Q that Voyager had assisted a year earlier. His suicide caused chaos in the Continuum. Now the status quo among the Q are fighting a violent battle against those Q who, like Quinn, believe in individualism. One of the repercussions of the conflict is the unusual frequency of supernovas, caused by spatial disruptions within the Continuum. To end the war, Q has decided to create a new breed of Q, with qualities that are "the best humanity has to offer" — hence, Q's proposition.
Back on Voyager, Chakotay questions the female Q about the war and they agree to join forces. She helps Voyager enter the Continuum, where Janeway encourages Q to mate with the female Q. While he considers the idea, Janeway visits the enemy camp to discuss a cease-fire. She offers a truce on Q's behalf, but the opposing Colonel decides to end the war by executing Q — and by sentencing Janeway to death for collaborating with the enemy.
Facing a firing squad, Q proclaims Janeway's innocence and asks the Colonel to set her free. The Colonel disregards the plea, but the "cavalry," in the form of the Voyager crew and the female Q, comes to the rescue. Q decides Janeway is right and asks the female Q to conceive a child with him. They touch their fingertips together and peace again reigns in the Continuum. Later, Q visits Janeway with his son, and asks the Captain to be the boy's godmother.