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Cedar Hill is an unincorporated community and census-designated place in San Juan County, New Mexico, United States. As of the 2020 census, Cedar Hill had a population of 1,130. The community is located on U.S. Route 550, near the Colorado border. Cedar Hill was originally known as Cox's Crossing. The name was chosen during a Literacy Society meeting by picking names out of a hat. A post office operated from 1892 to 1966.