There are 4 US Post Offices in Breathitt County serving a total of 12,836 residents equating to 3,209 residents per post office. It's estimated that approximately 20,488 packages are handled across the 4 county post offices annually. Breathitt County is a county located in the U.S. state of Kentucky. As of the 2010 census, the population was 13,878. Its county seat is Jackson, Kentucky. The county was formed in 1839 and was named for John Breathitt who was Governor of Kentucky from 1832 to 1834. Breathitt County was a prohibition or dry county, until a public vote on July 12, 2016 allowed the sale of alcohol."