Molly O'Brien was the daughter of Keiko and Miles O'Brien.
She was born aboard the USS Enterprise-D in 2368 in the ships's Ten Forward lounge, where she was delivered by Worf around stardate 45156. (TNG: "Disaster")
As a baby, Molly was said to be the spitting image of her father. (TNG: "Disaster", "The Game")
Later that year, Molly, together with her mother Keiko, was one of the crewmembers taken hostage by Ux-Mal criminals that had taken over the bodies of Data, Deanna Troi and her father, Miles O'Brien. Molly didn't stop crying and so caused some tension amongst the kidnappers. When the kidnappers left Ten Forward with some of the hostages, including Keiko, she asked the kidnappers for permission to leave Molly in the care of Diana Giddings. The family was later re-united in sickbay after Miles O'Brien had been freed from the influence of the aliens. (TNG: "Power Play")
In 2369, Keiko, visited the planet Marlonia where she found a specimen of Draebidium calimus, which she brought back to the Enterprise on her return trip. Moments before docking on the Enterprise, their shuttlecraft, Fermi, became enveloped in an energy field, and their subsequent emergency transport caused her body to be changed into a twelve year old. While Keiko's body was still older and larger than Molly, the difference was noticably less, and Molly had trouble adjusting to this change, refusing to acknowledge Keiko as her mother. This noticably upset Keiko and probably motivated her decision to assume her previous age, so that she would be accepted as a mother to her again. She was eventually returned to her normal state and was accepted as a mother by Molly again. (TNG: "Rascals")
Later that year, Molly moved aboard Deep Space 9, as her father got a new assignment there. (DS9: "A Man Alone")
Molly aged eighteen years before Miles could transport her back to the present
Molly aged eighteen years before Miles could transport her back to the present
In 2374, while on a picnic with her parents on a nearby planet, the eight year old Molly fell through a energy vortex. When the crew arrived to help, it was determined that she fell through a time portal 300 years into the past when the planet was uninhabited. When Chief O'Brien reactivated the portal, the calculations were off by ten years, and an eighteen-year-old version of Molly appeared.
Without Human contact for ten years, she was like a wild animal and had a difficult time adjusting to life on Deep Space 9. Molly was homesick for her planet, and the O'Briens tried to recreate the environment that Molly was used to on the holosuite. At first she made progress, but later became unmanageable. Starfleet wanted to commit her to a special facility. The O'Brien's decided to return her to the planet and send her back through the portal knowing that they would never see her again. When Molly went back, she found her eight year old self and sent her back through the portal to be reunited with her family. (DS9: "Time's Orphan")
Molly's younger brother, Kirayoshi, was born in 2373, and was carried by Kira Nerys. During this time, Molly sometimes referred to Kira as her aunt. (DS9: "Body Parts", "The Begotten")
Before the Dominion takeover of Deep Space 9 and the start of the Dominion War, Keiko took Molly and Yoshi to Earth for their safety. (DS9: "Call to Arms")
Both Molly and Kirayoshi moved back to Earth with their parents in late 2375, when Miles accepted a position as Professor of Engineering at Starfleet Academy. (DS9: "What You Leave Behind")
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