Ramba uchiverenga ndima iyi - Mumakwikwi eF2 muna 1979, Cheever akasiya Project Four akabatana nechikwata cheItaly cheOsella, achibva akunda katatu uye ari wechina pakupedzisira mumakwikwi avo eFA2 aishandisa motokari dzeBMW. Muna Osella akaenda kuFormula One, Cheever achityaira chikwata cheCosworth-powered FA1. Zvisinei, motokari yacho yakanga isina kuvimbika uye Cheever akakwanisa kupedza kamwe chete gore rose, nzvimbo yegumi nembiri pamakwikwi eimba yechikwata muItaly
. Kuchinja zvikwata kakawanda sezvaaiedza kukwira nzira yake kumusoro kwegridi, Cheever aive nemapoinzi mashanu-anopedzisa timu yeTyrrell muna 1982, uye matatu mapodhiyamu eLigier gore rakatevera, kusanganisira nzvimbo yechipiri pa1982 Detroit Grand Prix.