Just now tripped across this post. Although usually identified as a patch of the Army Air Corps, it's actually the patch of General Headquarters Air Force, an organization separate from the Air Corps, even though all it's personnel were assigned (by acto of Congress) to the Air Corps. Organized in March 1935, this was the first attempt to create a combat air arm that was independent of the central Air Corps control AND independent of Army field organizations. The Bureaucratic infighting nearly hobbled both organizations, a problem partially solved when Hap Arnold became commander of the Air Corps AND GHQAF. The real solution came in 1941 with the creation of the Army Air Forces (though personnel were still assigned - by acto of Congress - to the Air Corps, which no longer existed with a command structure.
Cheers,
Dana