What is the top level structure of these Chopped forces in the USAF? 
"Chopped" units are referred to as forces. The top-level structure of these forces is the Air and Space Expeditionary Task Force (AETF). The AETF is the Air Force presentation of forces to a CCDR for the employment of Air Power. Each CCDR is supported by a standing Component Numbered Air Force (C-NAF) to provide planning and execution of aerospace forces in support of CCDR requirements. Each C-NAF consists of a Commander, Air Force Forces (COMAFFOR) and AFFOR/A-staff, and an Air Operations Center (AOC). As needed to support multiple Joint Force Commanders (JFC) in the COCOM's Area of Responsibility (AOR), the C-NAF may deploy Air Component Coordinate Elements (ACCE) to liaise with the JFC. If the Air Force possesses the preponderance of air forces in a JFC's area of operations, the COMAFFOR will also serve as the Joint Forces Air Component Commander (JFACC).