The first Corvette rolled off the Chevrolet production line in mid-1953. Chevrolet intended the car to compete (in sales) with imported small sports cars. Initially, performance aspects were of secondary importance. Gradually, Chevrolet came to realize that racing success would help showroom sales.
Zora Arkus-Duntov began working for Chevrolet in 1953, and was quickly put in charge of high-performance development. In 1956, John Fitch was hired to help Chevrolet's racing team for Sebring in 1956. Early successes did indeed help improve the Corvette image, performance, and sales. Unfortunately, in 1957 General Motors signed on to the Automobile Manufacturers Association ban on factory-supported racing.
Small groups and individuals within Chevrolet continued development of racing options, with "back-door" help to outside racers. Results were mixed. In 1962, work began on a special series of lightweight Corvettes designed specifically for racing in Europe. When upper management learned of it, they forced the project to be stopped. Five Grand Sport Corvettes were completed, and sold or loaned to private racers.
At some point, the racing-support ban was lifted within General Motors. In the early 1980s, Chevrolet began development work on a Corvette GTP race car with a Lola T600 chassis and a Chevrolet V-6 turbo-charged engine. The two cars built usually qualified at or near the top, but rarely won, and often ended a race early. The program was abandoned at the end of 1988.
A new factory-based Corvette Racing team was initiated in 1996, with first races of the Corvette C5-R at the 24-hour race at Daytona in 1999. One car finished 3rd in class, followed by 2nd in 2000, and finally 1st in class and 1st overall in 2001. Factory-supported and individual racing continues today, with the Corvette C6-R and production Z06 options.
Recorded here are all known (to my research) top-three finished of Corvettes in sanctioned races. My sources are books and magazines, so this is an incomplete list. If you can point me to additional information please do!