Fitch started motorsport in 1949. He had long since made a name for himself in the SCCA sports car series when he drove his first race outside the USA in 1951. On an Allard - Cadillac he won the Peron Grand Prix in Buenos Aires . This success earned him a contract with the racing driver and racing team owner Briggs Cunningham . Cunningham, a wealthy entrepreneur who had built up a racing team in the late 1940s, tried to win the Le Mans 24 Hours with some financial investment . 1953 Fitch reached third place overall at Le Mans with Phil Walters as a partner. The vehicle was a Cunningham C5-R . In the same year he won the Sebring 12 Hours , again with Walters as a partner . In 1953 Fitch also drove the first of his two Formula 1 Grand Prix. At the Italian Grand Prix in Monza he drove a works HWM , but had to give up the race early after an engine failure.
Fitch had already tested a Mercedes-Benz 300 SL in 1952 and in 1955 Alfred Neubauer submitted a works contract to it . Fitch became a substitute pilot for the Formula 1 drivers, but was never used there. In Le Mans he was co-driver of Pierre Levegh and thus indirectly involved in the greatest disaster in motorsport. Before Stuttgart withdrew from the international motorsport scene, he won the sports car race in Dundrod with Stirling Moss . For Moss' private team, he also contested the 1955 Italian Grand Prix with its Maserati 250F and finished ninth, four laps behind the winner, Juan Manuel Fangio .
In 1956 Fitch returned to the USA and became a factory driver at Chevrolet . Since the US automaker's work was limited, the American was quiet, although he competed in the Sebring 12 Hours every year until 1964. After the end of his active career, Fitch worked in the management of race track operators and campaigned for the improvement of safety in automobile racing.