The Ist Air Commando was a self-contained unit outside the purview of 10th Air Force, and remained so until July 1945, when it was then incorporated into the 10th.
It was established by Hap Arnold following his meeting with Ord Wingate at the Quebec Conference in September 1943. Churchill had brought Wingate to the conference to prove that the British were hitting back at the Japanese in Burma - as a counter to 'Vinegar' Joe Stilwell's claims to the contrary.
Lt.Col Philip Cochran was put in charge, with Lt.Col John Alison as his 2IC. Cochran ran combat operations and Alison ran the supply and transport side.
For details of it's structure and aircraft complement see:
http://www.chindits.info/Thursday/AirCommando.htm