Allison first raced in the USAC Championship Car Series in 1970. Driving the No. 83 Greer Eagle 67-Offenhauser for Ansted-Thompson Racing in the 1970 Indianapolis 500, he finished 4th and won the 1970 Indianapolis 500 Rookie of the Year Award. He would have finished 20th in points, but because he was using a NASCAR license, he was ineligible for points. For the 1971 Allison drove the No. 84 Purolator Filters Coyote-Ford V8, finishing 6th in the Indianapolis 500. He also competed in the Rex Mays 150 at Milwaukee State Fairgrounds Speedway, the Schaefer 500 at Pocono International Raceway, and the California 500 at Ontario Motor Speedway, retiring from both. Allison was again ineligible for points.