Palmer was born in Chicago, Illinois on November 11, 1899, the oldest son of Colonel Charles Day Palmer. He graduated from the United States Military Academy in 1919 after an accelerated 3-year course. During World War II, as a brigadier general, he commanded VII Corps artillery, from the Normandy invasion to the Elbe. In January 1943 then Brigadier General Palmer was a passenger on a B-17 which landed in neutral Ireland. He was transferred across the border to Northern Ireland the next day.. Following the war he served as Director of Logistics, European Command, commanded the 82nd Airborne Division in 1950, followed by command of the 2nd Armored Division in 1951 and X Corps in Korea later that same year. He was promoted to Lieutenant General on 10 June 1952. While commanding the 2nd Armored Division based at Stuttgart- Vaihingen in Germany during 1952, Palmer was instrumental in establishing the Seventh Army Symphony Orchestra with a young conductor from within his ranks: Corporal Samuel Adler. In accordance with Adler's suggestion, Palmer staffed the orchestra with professionally educated musicians from within the Army itself. During the course of the next decade, Palmer's "soldier-musician ambassadors" distinguished themselves throughout Europe by supporting America's cultural diplomacy initiatives during the height of the Cold War. During his tenure as Director of Military Assistance, a scandal erupted over black market activities in Turkey involving military personnel. Palmer defended soldiers who refused to testify to the Senate by pointing out that the Uniform Code of Military Justice protected soldiers from self-incrimination. He caused controversy when in October 1960, while visiting Saigon, he said the United States was suspending military aid to Laos because of the "confused situation" in there, saying "we have not been sure who is responsible for anything." After two days of confusion, the U.S. embassy in Vientiane said the announcement had been incorrect and made without instructions from Washington, D.C. During his time as Vice Chief of Staff, in order to save money, he issued an order ending the horse drawn caissons in Arlington National Cemetery. However, his order was countermanded. He retired from the army in 1962. General Palmer died on November 10, 1973, at Walter Reed Army Medical Center in Washington, D.C. He never married, and was buried with his mother in Arlington National Cemetery, and was later joined by his brother.