Kammala jumla mai zuwa: Don gasar zakarun F2 ta 1979, Cheever ya bar Project Four kuma ya shiga kungiyar Italiya ta Osella, inda ya ci nasara uku kuma ya zama na hudu a cikin FA2 mai amfani da BMW. A cikin Osella ya koma Formula One, Cheever yana tuka ƙungiyar ta Cosworth-powered FA1. Koyaya, motar ba ta da aminci kuma Cheever ya sami nasarar gamawa ɗaya kawai a duk shekara, na goma sha biyu a tseren gida na ƙungiyar a
Italiya ce. Sauya ƙungiyoyi akai-akai yayin da yake ƙoƙarin hawa hanyarsa ta hanyar grid, Cheever yana da maki biyar da aka kammala don ƙungiyar Tyrrell a cikin 1982, da kuma podiums uku don Ligier a shekara mai zuwa, gami da matsayi na biyu a Babban Prix na Detroit na 1982.