The governor's office said it would not release information because it considers the baby's birth a private family matter.
The father is Levi Johnston, a former hockey player at Alaska's Wasilla High School.
Palin announced on Sept. 1, the first day of the Republican National Convention, that her unwed daughter was pregnant. The campaign issued a statement saying Bristol "and the young man" would get married.
Levi Johnston's mother eventually disclosed that her 18-year-old son was the father. The following week, the young man attended the convention in St. Paul, Minn. when Palin accepted the nomination as John McCain's running mate.
The announcement that Bristol, 17 at the time, was pregnant immediately drew concerns that it could damage Palin's credibility as a religious conservative. It also foreshadowed a troubled campaign for Palin, who drew large crowds at rallies but was criticized for her composure in news interviews and for her experience level.
Sherry Johnston, Levi's mother, said in October that Bristol and her son were considering a summer wedding.
Levi Johnston told The Associated Press that month that he and Bristol loved each other and wanted to get married. Johnston, who dropped out of high school to take a job on the North Slope oil fields as an apprentice electrician, said he was a little shocked to learn that Bristol was pregnant but quickly warmed to the idea of being a father.
He said the two had planned to get married even before Bristol became pregnant.
Johnston, an avid hunter, hinted at the time that they were expecting a boy. He said he was already looking forward to taking the boy hunting and fishing.
Johnston's mother was arrested on felony drug charges this month after state troopers served a search warrant at her Wasilla home. According to authorities, she sent text messages to two police informants in which she discusses making drug transactions involving OxyContin, a strong prescription painkiller.
Sarah Palin and her husband, Todd, have five children ranging in age from Trig, 7 months, to Track, 19. In between are Willow, 14; Piper, 7; and Bristol.
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