Britta gave birth to a baby girl last Friday, according to Sarah Palin biographer Joe McGinniss.
A spokesperson for the Palin family has not yet confirmed the birth.
Track and Britta have dated since they were in high school and tied the knot in May in Hatcher Pass, AK.
Former Alaska Governor Sarah's daughter Bristol and her ex-fiancé Levi Johnston had their first child Tripp in 2008.
Bristol has said that becoming a mother at such a young age "cut short" her teenage years.
A documentary on Sarah Palin's life and political career is to be given an early DVD release because of its poor box office showing.
> Bill Maher: 'Sarah Palin can win presidency'
Watch a trailer for the Sarah Palin documentary The Undefeated below: