There are 3 US Post Offices in Wheeler County serving a total of 1,483 residents equating to 494 residents per post office. It's estimated that approximately 2,367 packages are handled across the 3 county post offices annually. Wheeler County is a county located in the U.S. state of Oregon. As of the 2010 census, the population was 1,441, making it the least populous county in Oregon. The county seat is Fossil. It is named in honor of Henry H. Wheeler, an early settler who owned a farm near Mitchell. Wheeler County is known for having a large deposit of fossils, the most extensive in the state."