La Plata County is one of the 64 counties in the U.S. state of Colorado. As of the 2010 census, the population was 51,334. The county seat is Durango. The county was named for the La Plata River and the La Plata Mountains. "La plata" is the Spanish language word for "silver".La Plata County comprises the Durango, CO Micropolitan Statistical Area.The county is home to Durango Rock Shelters Archeology Site, the type site for the Basketmaker II period of Anasazi culture.