“That’s right, one lucky woman will win the ultimate chance at starting or building her family,” said a contest announcement issued in April by Long Island I.V.F., a clinic in Melville that offers in vitro fertilization to women who are having difficulty conceiving.

Contestants were asked to submit “the most emotional or entertaining essays and homemade amateur videos” explaining why they wanted a free round of I.V.F. “Make us laugh with you or cry with you,” the announcement said. “Tell your story straight from the heart.”

The winner, Jessica Upham of West Babylon, N.Y., submitted a video that showed her repeatedly injecting her abdomen with hormones and later weeping on her bed as a clinician delivered bad news. When she found out that she won the contest — a doctor holding balloons knocked on her door the day after Labor Day — she “just lost it,” she said in an interview.

“I feel inadequate that I can’t provide this to my husband the natural way,” said Ms. Upham, 37, who has a son conceived through I.V.F. and is receiving the free embryo implant this month. The prize, she said, is “a wonderful opportunity that I wouldn’t otherwise have.”