Claiborne was born on July 2, 1917 in McRae, Arkansas. His father was Arthur Smith Claiborne Jr., a cotton farmer, and his mother was Minnie King Claiborne, a schoolteacher in Little Rock, Arkansas. According to Harry, the Ku Klux Klan's grand wizard once criticized Harry's father, Arthur, for being the only white farmer in the region who was not a member of the organization. Arthur responded, "I won't join any organization whose members need to wear hoods over their faces." After later saving an immigrant farmer from a lynching, Arthur knew the KKK would return for retribution and waited at the immigrant's farm with a shotgun. When the KKK arrived, one of their members approached a barn with a lit torch, but Arthur fired a round of buckshot into him and knocked him from his horse. According to Harry, "Never again was a man lynched by the KKK in his community because they knew they would have to answer to Claiborne." The event had a profound impact on Harry's worldview.