During the 1970s and 1980s, Chevallier designed and built road racing motorcycles using Yamaha engines and campaigned them in the Grand Prix world championships.
His brother Olivier Chevallier rode the bikes until he was killed while competing at the Grand Prix of Le Castellet in 1980.
In 1982, Didier de Radiguès rode a Chevallier-designed bike to victory in the 350cc Yugoslavian Grand Prix and finished the season in second place in the F.I.M.
His Chevallier teammate Eric Saul won the Austrian Grand Prix and finished the championship in fourth place.
In 1983, three of Chevallier's motorcycles ridden by de Radiguès, Thierry Espié, and Jean-François Baldé, finished in the top ten of the F.I.M.