Triumph began planning a successor to the TR3 as early as 1956. At the time, the company was facing a number of challenges. Lack of capital to fund development was partly relieved by the sale of Triumph's tractor division to Massey-Harris of Canada. A long overdue refresh of their small sedans was further complicated by the departure of chief stylist Walter Belgrove over a disagreement with the direction of the redesign.[4]

After being introduced to Giovanni Michelotti, Triumph managing director Alick Dick invited the Italian designer to produce a concept car for the British company.[4] Michelotti responded with the Triumph TR3 Speciale, also called the "TR Dream Car".[5]

Built by Vignale on an unmodified TR3 chassis, Michelotti's TR Dream Car incorporated many styling cues from contemporary American practice, including tailfins, a full width grille, lidded headlamps in the tops of the front wings, and a two-tone paint treatment.[4][6] The TR3 Speciale debuted at the Geneva International Motor Show in March 1957.[7]Triumph deemed the car too expensive to put into production, but did give the job of designing the new Triumph Herald to Michelotti