Agase was born in Chicago to an Assyrian father, Charles Agase (1883–1959), and an Armenian mother, Elsie Darwitt (1892–1971). Both were born in Persia. He attended Evanston Township High School, but only played on the school's varsity football team in his senior year. After graduating, he attended the University of Illinois and played college football there as a right guard in 1941 and 1942. In a 1942 game against the University of Minnesota, Agase scored two touchdowns for the Fighting Illini, becoming only the second guard in college football history to accomplish that feat. The first touchdown came in the second quarter, when Agase stripped the ball from Minnesota's Bill Daley and ran it back 35 yards. The second was a fourth-quarter fumble recovery in the end zone to give Illinois a 20–13 victory. In another game against Great Lakes Naval Training Station, a military team, Agase had 22 tackles. Under coach Ray Eliot, Illinois finished the season with a 6–4 win-loss record. Agase was named an All-American after the season.