Born near Beaune, in the Côte-d'Or département of France where his Swiss parents had emigrated to a few years earlier, he was the younger brother of Louis and Arthur. Louis was the first to emigrat to the United States and once he had earned enough money, in 1902 he sent for Gaston and Arthur to join him. Once there, Gaston worked as an automotive mechanic and joined his brother in auto racing.
In 1916, Gaston Chevrolet became a partner with his brothers in the Frontenac Motor Corporation, pioneering the use of aluminum and other leading edge concepts in racing construction.
He started racing in 1916 when he entered the Indy 500. However he failed to qualify. Then, the following year, he started to post some good results. Third in the grueling 250-mile race on the Cincinnati board track, won by his brother Louis, he also posted two seconds and a third in sprint races at Chicago.
He was suspended by the AAA in 1918 for running in outlaw races, but regained his license in 1919 and became one of the leading drivers for the Frontenac team. His season started slowly. At the Indy 500 he finished in tenth place while brother Louis finished seventh but he then scored three straight victories, first at Sheepshead Bay in a 100 mile race, then Uniontown, a 225 mile event, and then back at Sheepshead for a 150 mile race. He finished sixth in the national championship.
Frontenac had eight cars with the new 183 cubic inch engines at the 1920 Indy 500. Gaston drove a careful race, roughly keeping pace with the leader but preserving his car. When they faltered he made up a two-lap deficit to win. In the process, he became the first driver in the history of the 500 mile race to go the distance without making a tire change.
Gaston drove six more times that year, winning a 100-mile match race against veterans Tommy Milton and Ralph Mulford. Then with winter approaching, racing moved to the West Coast and in the Beverly Hills 200-Mile Race at the Los Angeles Speedway board track in Beverly Hills, California, Gaston was leading when he crashed on lap 146. He died from his injuries.
Gaston Chevrolet is interred next to his brothers in the Roman Catholic Holy Cross and Saint Joseph Cemetery in Indianapolis, Indiana.