Kammala jumla mai zuwa: Allison ya fara tsere a gasar Championship Car Series a shekarar 1970. Gudanar da No. 83 Greer Eagle 67-Offenhauser don Ansted-Thompson Racing a cikin
1970 Indianapolis 500, ya gama na 4 kuma ya lashe 1970 Indianapolis 500 Rookie na shekara Award. Da ya gama na 20 a maki, amma saboda yana amfani da lasisin NASCAR, bai cancanci maki ba. Don 1971 Allison ya tuka No. 84 Purolator Filters Coyote-Ford V8, ya gama na 6 a cikin Indianapolis 500. Ya kuma yi gasa a cikin Rex Mays 150 a Milwaukee State Fairgrounds Speedway, da Schaefer 500 a Pocono International Raceway, da California 500 a Ontario Motor Speedway, yana yin ritaya daga duka biyun. Allison ba ta sake samun maki ba.