Stevenson drove in the AAA and USACChampionship Car series, racing in the 1949-1954, 1960–1961, and 1963-1965 seasons with 54 starts, including the Indianapolis 500 races in 1951-1954, 1960–1961, and 1963-1965. He finished in the top ten 37 times, with four victories, two of them coming in the 1952 season when he won the AAA National Championship.
In 1951 Stevenson drove a Nash-Healey course (pace) car for the grueling 2,000-mile (3,219 km) Carrera Panamericana race. This endurance event is described as one of the most dangerous automobile races of any type in the world, and Stevenson had to be ahead of the racers to ensure the way was clear. In both 1952 and 1953 he won the sedan class driving a "well-prepared" Lincoln Capri, the only two-time winner in the history of the Carrera Panamericana.
The Indianapolis 500 was part of the FIA World Championship from 1950 through 1960. Drivers competing at Indy during those years were credited with World Championship points and participation. Chuck Stevenson participated in five World Championship races, but scored no World Championship points.