Schiller was a speedboat champion in his native Switzerland before turning to sports car racing, finding success during the mid-1950s.

He then switched to single seater cars, starting in hillclimbing before moving up to circuit racing.

He first appeared in Formula One at the beginning of 1962 with Ecurie Nationale Suisse, driving their three-year-old Porsche in the Brussels Grand Prix, where he finished 8th on aggregate after the three heats.

Under the Ecurie Filipinetti banner but still driving the same Porsche, Schiller failed to qualify at the Naples Grand Prix, largely because only 10 cars were permitted to take the start.

Schiller made one appearance in Formula One in 1963, finishing 3rd at Pau but five laps down, again in the old Porsche, before returning to sports cars.