McGlockton played college football at Clemson University, and was drafted by the Los Angeles Raiders in the 1st round (16th overall) of the 1992 NFL Draft. He played six seasons with the Raiders, earning all four of his Pro Bowl appearances with them. McGlockton also played for the Kansas City Chiefs, the Denver Broncos, and ended his career by playing one season with the New York Jets.
At the start of 2007, McGlockton was a training camp intern coach with the NFL Europan team the Amsterdam Admirals during their training camp in Tampa, Florida. Chester is a co-owner of D1 Sports Training in Greenville, SC.