Bill Thomas had become pretty successful modifying various Chevrolets products for track use. After some success racing Corvettes in the lats 50s, in 1960, he went on to start his own company that turned Chevy IIs and Corvairs into viable track cars. He became so good at it, that by 1963, he had the attention of Vince Piggins, then-head of the GM Performance Product Group. Piggins asked Thomas to develop a concept car utilizing GM Performance parts.
Thomas quickly acquired a 327 ci Corvette engine, a Muncie transmission, and the gear to assemble an independent rear suspension. Other parts such as spindles and brakes were also pulled directly from the GM Performance parts bins. Thomas relied heavily on his lead fabricator Don Edmonds to design and build the chassis. Edmonds developed most of his cars with very little in the way of formal drawings. The Cheetah was no different. Edmonds laid the components out on the shop floor and chalked out the basic chassis outline. Even later in development, there were very few control drawings for the Cheetah, and those that existed only had some cursory dimensions on them.