Peterson began his motor racing career in kart racing, traditionally the discipline where the majority of race drivers begin their careers in open-wheel racing. After winning a number of karting titles, including two Swedish titles in 1963 and 1964, he moved on to Formula Three, where he won the Monaco Grand Prix Formula Three support race for the 1969 Grand Prix. Later that year he won the FIA European Formula 3 Championship and moved up into Formula One, racing for the March factory team. In his three-year spell with the team, he took six podiums, most of which were scored during the 1971 Formula One season in which he also finished as runner-up in the Drivers' Championship.