There are 4 US Post Offices in Concho County serving a total of 4,046 residents equating to 1,012 residents per post office. It's estimated that approximately 6,458 packages are handled across the 4 county post offices annually. Concho County is a county located on the Edwards Plateau in the U.S. state of Texas. As of the 2010 census, the population was 4,087. Its county seat is Paint Rock. The county was founded in 1858 and later organized in 1879. It is named for the Concho River."