As an amateur cyclist Georges Chappe was part of the quartet that won the 100 kilometres team time trial at the 1963 UCI Road World Championships in Ronse, Belgium. That same year Chappe also won silver in the road team time trial at the Mediterranean Games before finishing sixth in the 100 kilometres team time trial at the 1964 Tokyo Olympics. Chappe then turned professional, riding in seven editions of the Tour de France. He had a love-hate relationship with the race, winning a stage in 1968, abandoning in 1965 and 1969, and finishing in last place in 1971, earning the lanterne rouge. During his professional career Chappe also rode in three editions of the Vuelta a España, and won two editions of the Paris–Camembert semi-classic race (1967, 1970) and the two-day stage race the Critérium International in 1970.