Chinook is a city in and the county seat of Blaine County, Montana, United States. The population was 1,185 at the 2020 census. Points of inter…Chinook is a city in and the county seat of Blaine County, Montana, United States. The population was 1,185 at the 2020 census. Points of interest are the Bear Paw Battlefield Museum located in the small town's center and the Bear Paw Battlefield, located 20 miles south of Chinook.