There are 6 US Post Offices in Blaine County serving a total of 6,089 residents equating to 1,015 residents per post office. It's estimated that approximately 9,719 packages are handled across the 6 county post offices annually. Blaine County is a county located in the U.S. state of Montana. As of the 2010 census, the population was 6,491. Its county seat is Chinook. The county was named in honor of James G. Blaine, former United States Secretary of State. It is south of the Canada\u2013US border with Saskatchewan.