Parmer County is a county located in the southwestern Texas Panhandle on the high plains of the Llano Estacado in the U.S. state of Texas. As of the 2010 census, the population was 10,269. The county seat is Farwell. The county was created in 1876 and later organized in 1907. It is named in honor of Martin Parmer, a signer of the Texas Declaration of Independence and early judge. Parmer County is one of 10 prohibition, or entirely dry, counties in the state of Texas.