Eunice is a city in Lea County, New Mexico, United States. The population was 2,922 at the 2010 census. The mayor of Eunice, as of March 2018, was Billy Hobbs. A URENCO USA National Enrichment Facility, which uses Zippe-type centrifuge technology to enrich uranium, has been in operation 5 miles east of Eunice since 2010.