The Enterprise stops at Starbase 313, and Geordi La Forge welcomes on board Dr. Leah Brahms, one of the designers of the Galaxy class starships. He has much anticipation at meeting her, having previously developed a crush on the Doctor after working with a holodeck simulation of her during a prior mission (see "Booby Trap"). However, this excitement is quickly replaced by frustration when he discovers that Dr. Brahms is annoyed that Geordi has been making modifications to the starship engines she designed.
Meanwhile, the Enterprise encounters a strange space-faring lifeform. Without provocation, the alien creature attacks the vessel, and Captain Picard orders the crew to respond with a low intensity phaser burst which unfortunately kills the lifeform. Scanning the dead creature, Data discovers another smaller lifeform inside it. The reason for the larger creature's attack becomes clear: it was attempting to protect its unborn child.
The bridge crew prepare to save the alien fetus by using the phasers to perform a Caesarean section. The procedure is successful, and the infant wriggles free into space. Mission accomplished, the Enterprise begins to depart, but the newborn follows and attaches itself to the ship. It has imprinted on the Enterprise as though the ship is its mother, and once attached it begins to drain the starship's energy.
While these events have been playing out, Geordi has been making some attempts to get to know the real Leah Brahms. However, Leah has remained unimpressed with Geordi's engine modifications, and is unresponsive to his clumsy attempts to get closer. Then, he discovers that somehow, despite the supposed accuracy of the holodeck simulation of Dr. Brahms, that she is not a single woman but is in fact married. A discouraged Geordi later heads to Ten Forward to seek sympathy from the bartender, but Guinan points out that it is not Leah's fault that she has failed to live up to Geordi's mistaken expectation.
At a brief staff conference it is determined the Enterprise should determine where the mother was going, with the idea that this may be the best habitat for the infant. Once there, the crew will attempt to blow the alien off the ship by depressurizing one of the shuttle bays.
At the conclusion of the meeting, Leah asks Geordi if she can take a look at files of Geordi's engine modifications. Geordi agrees, momentarily forgetting that Leah could stumble across his old holodeck simulation of her. Once he realizes his error, Geordi hurries to the holodeck and just in time to find a very angry Leah Brahms standing in front of her own simulation, which is chatting about how close she feels to Geordi. Understandably, Dr. Brahms feels that her privacy has been invaded. Geordi eventually calms her down and claims that the only thing he's guilty of is offering his friendship.
The ship reaches the mother's destination: an asteroid belt containing those mineral elements the creature needs to survive. Unfortunately, the plan to blow the creature off the ship fails. Eventually Leah and Geordi, by working together, reason that by changing the frequency of the ships power might have the effect of "souring the infant's milk". This solution works, and having had some success combining their efforts, Geordi and Leah come to an understanding of one another.