The first Cunningham to bear the C-3 designation was built in 1951 on a C-1 chassis at a cost of $15,000, proving it unfeasible in an American market that, even in the upper income ranges, was not prepared to go to five figures. In addition, the car did not approach the deluxe level of finish Briggs had in mind for a Cunningham road car, as it was essentially a competition roadster with a hardtop.

Briggs then contracted with Carrozzeria Vignale of Turin, who would build bodies on the C-2 chassis. Rolling chassis were shipped to Turin from West Palm Beach and fitted with either coupe or roadster bodies, then returned to Florida for final finishing and delivery.

The car's dimensions were such that it was smaller than the vast majority of American cars yet larger than the Ferraris and Maseratis it most resembled, while the styling was typical of Giovani Michelotti's designs, restrained and well-proportioned, with minimal use of brightwork. The interior, described by a contemporary writer as "oozing luxury", was functional and beautifully finished. Performance was beyond practically any other American car of the time.

While it is not known exactly how many C-3s were built, Cunningham himself estimated the figure at perhaps thirty. The low production figures prompted the IRS to withdraw Cunningham's status as a manufacturer, a move that eventually caused the demise of the company's racing operations.