Towards the end of the 1963 season, Keniss began to realize that the once indomitable T2 chassis was starting to become obsolete. In late October of 1963, they began development of a new chassis built around the Cosworth KR62R, an updated KR62. The new chassis, originally dubbed the T2C, was lighter, smaller and faster than the T2 and T2B, and as a result could use a smaller fuel tank. The chassis, now dubbed the T3 (and later the T4 in 1965), was first tested at the Nurburgring on January 3rd 1964. It proved to be very fast in a straight line, but slightly slower than the Ferraris through the corners. Over the course of the 1964 and 1965 seasons, the car was driven by three drivers. Alex Clark was the primary driver, and the only driver who had scored wins for Keniss at that point. Two other drivers, Tom Roth and Vincent Almore, drove the car as well. Roth was forced to retire from Formula One in 1964 following a severe accident at Spa which resulted in him severing his spinal cord. Vincent Almore was then pulled out of his contract with BRM and joined Keniss for the following race in France. The car scored One win, Three Podiums and One Pole Position in 1964, and Two wins, Seven Podiums and Two Pole Positions in 1965. Vincent Almore also scored the first of his 21career wins in 1965, at Watkins-Glen. The car was supplanted by the T5 in 1966.