According to AMG it was written by Fred Rose, as in Acuff-Rose Publishing Company.

Fred Rose signed Hank Williams as a writer in 1947 where he joined Pee Wee King and others. They taught Hank Williams the art of songwriting.

"... Williams signed to MGM in 1947, Rose became his manager and producer, also co-writing classics including "A Mansion on the Hill," "Kaw-Liga," "Crazy Heart," "Settin' the Woods on Fire," "I'll Never Get Out of This World Alive," and "Take These Chains From My Heart." Rose also possessed an extraordinary gift for placing Acuff-Rose material..."

So, let's extend the list of Country songwriters to Harlan Howard, Cindy Walker, Willie Nelson and Fred Rose.