There are 5 US Post Offices in Cheatham County serving a total of 38,057 residents equating to 7,611 residents per post office. It's estimated that approximately 60,743 packages are handled across the 5 county post offices annually. Cheatham County is a county located in the U.S. state of Tennessee. As of the 2010 census, the population was 39,105. Its county seat is Ashland City. Cheatham County is part of the Nashville-Davidson\u2013Mufreesboro\u2013Franklin, TN Metropolitan Statistical Area."