Gillem was the first son of Lieutenant General Alvan Cullom Gillem Jr. (1888–1973) and Virginia (Harrison) Gillem (December 18, 1895 – October 25, 1964). He had two siblings, Richard D. Gillem (who became a lieutenant colonel in the United States Army) and Mary.
Military career
Gillem enlisted in the United States Army at Fort Monroe, Virginia, in 1935. He received a congressional appointment to the United States Military Academy for the fall of 1936, from which he graduated with the rank of second lieutenant in the spring of 1940.
Gillem immediately entered pilot training in the fall of 1940 and graduated in March 1941 as a first lieutenant. He then served in Texas as a pilot-instructor from March 1941 to March 1943; he was promoted to major in 1943. In April 1943 he went overseas as a staff officer at headquarters of the Mediterranean Allied Air Forces in North Africa. Later he was transferred to the 31st Fighter Group in Italy where he learned to fly Spitfires and P-51 Mustangs, and was credited with shooting down three enemy planes in air-to-air combat. He was promoted to lieutenant colonel in May 1944. In June he returned to the United States to serve in the Plans Division of the Headquarters, Army Air Forces in Washington, D.C.
In July 1963 he was transferred to Homestead Air Force Base, Florida, where he became commander of the 823d Air Division. In August 1963 he was promoted to major general.
In May 1964 Gillem was transferred to SAC headquarters at Offutt Air Force Base, Nebraska, as Deputy Director of Operations. In July 1965 he was named Director of Operations (later redesignated as Deputy Chief of Staff, Operations) in July 1965.
In June 1968, upon promotion to lieutenant general, he took over the 3d Air Division at Andersen Air Force Base, Guam, where for the following 26 months he commanded SAC's B-52 and KC-135 forces operating in the Western Pacific and Southeast Asia. In April 1970 the 3d Air Division was redesignated the Eighth Air Force.
Gillem became the 12th commander of Air University on August 1, 1970, retiring on November 1, 1973, after serving there for three years.