There are 5 US Post Offices in Hamilton County serving a total of 8,550 residents equating to 1,710 residents per post office. It's estimated that approximately 13,647 packages are handled across the 5 county post offices annually. Hamilton County is a county located in the U.S. state of Illinois. According to the 2010 census, it has a population of 8,457. Its county seat is McLeansboro. It is located in the southern portion of the state known locally as \"Little Egypt\"."