Arapahoe County Government is housed in Colorado s first county and is one of the largest counties in Colorado with a population of more than 527,000. Arapahoe County was named for the Arapaho Indians, who along with the Cheyenne Indians, occupied most of Colorado when it was only a territory. The county employs approximately 1,800 people and features a nearly $294 million budget. Arapahoe County is governed by the Board of County Commissioners. The commissioners, along with the assessor, clerk and recorder, coroner, district attorney, sheriff and treasurer are elected by voters to administer county services. Arapahoe County Government is located in Littleton, Colo.