John Albert Adams (November 28, 1937 â August 8, 1995) was a professional American football fullback in the National Football League (NFL). He played for five seasons for the Chicago Bears (1959âÂÂ1962) and the Los Angeles Rams (1963). Adams was a fifth round selection (57th overall pick) of the Bears in the 1959 NFL draft out of California State University, Los Angeles.