The Rhea County commissioners approved the request 8-0 Tuesday. Commissioner J.C. Fugate, who introduced the measure, also asked the county attorney to find a way to enact an ordinance banning homosexuals from living in the county.
"We need to keep them out of here," Fugate said.
The vote was denounced by Matt Nevels, president of the Chattanooga chapter of Parents, Family and Friends of Lesbians and Gays.
"That is the most farfetched idea put forth by any kind of public official," Nevels said. "I'm outraged."
Last year, the U.S. Supreme Court struck down Texas' sodomy laws criminalizing gay sex as a violation of adults' privacy.
Rhea County has been in the headlines before in matters of ideology and law.
Dayton, Tennessee, was the site of the so-called "Monkey Trial" in 1925, in which John T. Scopes was convicted of teaching Charles Darwin's theory of evolution - in defiance of state law - a verdict the state's Supreme Court later threw out on a technicality.
The trial mesmerized the nation and decades later was the basis for the 1955 play and 1960 movie "Inherit the Wind," written then in part as a vehicle for protesting the threats to freedom of thought posed by anti-Communist hysteria in the 1950s.
Rhea County - one of the most conservative counties in Tennessee - still holds an annual festival commemorating the trial.