Going to the university at Riegels' suggestion, Chapman starred in football for the Golden Bears, being named an All-American for the 1937 Pacific Coast Conference and national champion "Thunder Team", which went on to win the 1938 Rose Bowl; the last time California has won the game. Nicknamed the "Tiburon Terror", Chapman was also an All-American baseball player in college.
He joined the Navy for World War II after the 1941 season, and served as a pilot and flight instructor in Corpus Christi, Texas. He returned to the Athletics in late 1945, and was named to the AL All-Star team in 1946. But he never quite returned to his pre-war level of play; apart from 1949, when he batted .278 with 24 HRs (tied for third in the AL) and 108 RBI (fifth in the AL), he never exceeded a .261 average. He was traded to the Cleveland Indians in May 1951, and ended the year with a .215 batting mark; he left the major leagues at the end of that season, but played three more years for the Oakland Oaks of the Pacific Coast League. In an 11-season major league career, Chapman posted a .266 batting average with 180 home runs, 773 RBI, 754 runs, 1329 hits and 41 stolen bases in 1368 games.