Three Rivers is a city in Live Oak County, Texas, United States. The population was 1,878 at the 2000 census. The city is named for its proximity to three rivers, the Atascosa River, the Frio River, and the Nueces River (the Atascosa joins the Frio north of the city, while the Frio joins the Nueces south of the city). Originally named Hamiltonburg, the city name was changed when mail meant for the city was accidentally delivered to Hamilton, Texas instead.