When Captain Picard asks Geordi to escort a visitor, Dr. Leah Brahms, aboard the Enterprise, Geordi is thrilled. He confides to Guinan that Leah, the woman who designed the U.S.S. Enterprise's engine, is the woman of his dreams.

During a crisis, he recreated a Holodeck image of Dr. Brahms to help him and felt a strong rapport with her. But when the real Leah finally transports aboard, he is crushed to discover that she is cold, cerebral and humorless. She puts him through his paces, icily examining and criticizing the adjustments he has made to the engine she helped design.

Meanwhile, Picard and the crew discover a large energy source floating in space. When they approach the creature to learn its origin, it suddenly latches onto the starship, bombarding the ship with deadly radiation. In defense, Picard fires the ship's phasers to release the U.S.S. Enterprise from the alien's clutches. Picard is saddened when the phaser assault kills the lifeform, but he is intrigued when Data detects another energy reading within it. To everyone's surprise, Data explains that they have discovered a "baby" struggling to escape its dead mother's womb.

Later on, Geordi hopes for a fresh start with Dr. Brahms when she agrees to have dinner with him, but she is put off by his informal demeanor and leaves him alone with his homemade pasta getting cold. The next morning, Leah arrives in an improved mood. Geordi is happy to finally be working closely with his dream woman — until she informs him that she is married. On the Bridge, Beverly and Worf perform a Cesarean section with phasers in order to free the alien offspring from its dead mother. Unfortunately, it begins to follow the U.S.S. Enterprise, thinking the starship is its mother and nurses on its hull. The crew tries to devise a plan to deliver the alien baby to its mother's destination, a nearby asteroid belt, and Geordi and Leah are forced to work together again to increase the ship's energy sources to provide for the baby until they reach their destination. Things go well until Leah accidentally discovers Geordi's Holodeck recreation of her. Infuriated, she chastises Geordi for using her as a plaything. Angered by her accusations, Geordi pleads guilty only to wanting to be her friend.

Upon reaching the asteroid belt, the crew tries to disengage the baby creature, but it will not let go. At this point several larger energy beings approach the Enterprise as if to attack the ship. Working together one last time, Geordi and Leah devise a plan to alter the frequency of the energy the creature is feeding on to make it foreign to the baby and send it away. With seconds to spare, the baby creature lets go, and is enveloped by the larger creatures who float off together. Later, in the Ten-Forward, Geordi and Leah exchange apologies and laughs about the "Holodeck incident," having reached a new level of understanding through working together.