"The Q and the Grey" is the 11th episode of the third season of Star Trek: Voyager, the 53rd episode overall.
Captain Kathryn Janeway is surprised when Q appears in her quarters one night. Q is intent on Janeway becoming the mother of his child, and plies the Captain with gifts in an attempt to win her affections. Janeway is not amused, and demands that Q leave immediately. Q is persistent, claiming that he could have chosen any female in the galaxy and that his desire for Janeway should be regarded as an honor. Janeway continues to insist that Q leave, and eventually he does.
However, Q's absence does not last long, as he abducts the captain and takes her to the Q Continuum, now appearing as an American Civil War period piece, with Q dressed in the uniform of a Union officer. Confederate soldiers fire on them, and Q is wounded - surprising Janeway to no end. Q's sense of urgency becomes apparent: There is a real civil war brewing among the Q race, and Q hopes that he and Janeway can bring a child into the continuum (which has not had a natural birth in billions of years and Q claims they have always existed) to avert the war. Q explains that the civil war started because of him - he leads a faction of the Q which advocates individual freedom, rather than the status quo enforced by the Q at large. Q shows Janeway the carnage that the war has inflicted on his group (represented by a refugee camp in which hundreds of wounded Q, all appearing as Union soldiers, are suffering).
The fighting breaks out again, and the Q authorities (represented as Confederate soldiers) arrive and capture Q and Janeway. The Q leader, appearing as a Confederate colonel, intends to execute them both, to serve as an example to the rest of Q's freedom faction.
On Voyager, the remaining crew have been observing dozens of supernovae taking place throughout the area - many more than should be occurring. A Q female arrives and says that the civil war among the Q is the cause. The female Q is abrasive and insulting to the crew, and she explains that she is Q's ex-wife. As the civil war continues to rage, the female Q realizes she has lost her powers, and is forced to enlist the aid of the Voyager crew. She helps them reach the Q continuum by flying into a supernova, and provides the Voyager crew with Q weapons which they use to free Q and Janeway. Q and his wife resume their relationship and decide to become parents themselves, thus providing the Q continuum with "new blood" which they hope will revitalize the species.
Captain Janeway is witness to the two Q mating. To mate they simply touched fingers, causing a flash similar to the effect used when a Q conjures something up. A moment later Q tells his wife he knows he was good. "That's it?!" a surprised Janeway asks. "You had your chance," Q responds.
Q returns later to Janeway's quarters with his son and asks her to be his godmother, which she accepts.
Given the Civil War theme the episode title is likely a reference to the 1982 miniseries The Blue and the Gray (miniseries).
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