There are 7 US Post Offices in Dickenson County serving a total of 15,016 residents equating to 2,145 residents per post office. It's estimated that approximately 23,967 packages are handled across the 7 county post offices annually. Dickenson County is a county located in the Commonwealth of Virginia. As of the 2010 census, the population was 15,903. Its county seat is Clintwood.