Breckinridge was elected Attorney General of Kentucky in 1959 when Bert T. Combs led the Democratic ticket to victory. He served his first term in that office in 1960–1964. In that first term Breckinridge served on the National Conference of Commissioners on Uniform State Law and was a delegate to the Democratic National Convention in 1960. Under state law at that time Breckinridge could not run for a second consecutive term as attorney general. He ran that year for Lieutenant Governor of Kentucky but lost in the Democratic primary to Harry Lee Waterfield. After that defeat Breckinridge returned to his law practice and began planning for a return to public office.