Anton Chico, or Anton Chico Abajo or Anton Chico de Abajo, is a census-designated place in Guadalupe County, New Mexico, United States. Its population was 188 as of the 2010 census, of which 167 were Hispanic in origin. Anton Chico has a post office with ZIP code 87711. New Mexico State Road 386 passes through the community. Anton Chico is listeā¦Anton Chico, or Anton Chico Abajo or Anton Chico de Abajo, is a census-designated place in Guadalupe County, New Mexico, United States. Its population was 188 as of the 2010 census, of which 167 were Hispanic in origin. Anton Chico has a post office with ZIP code 87711. New Mexico State Road 386 passes through the community. Anton Chico is listed in the National Register of Historic Places.