Klien started his motorsport career in his early teens. He raced in karting championships in both Austria and Switzerland. He moved up to Formula BMW. He won several titles in lower Formula series. Klien moved into Formula One in . He drove for the Jaguar Racing team, alongside Mark Webber. At the end of 2004, Jaguar sold its Formula One team to Red Bull. The team was renamed "Red Bull Racing". Klien shared a race seat with Italian Vitantonio Liuzzi. He stayed at Red Bull for season. 