Csonka began his football career at Stow High School as the starting fullback on the 1963 Stow Bulldogs squad that won the Metropolitan League of the Akron, Ohio, area championship under coach Dick Fortner.
Csonka became a running back by accident. Because of his size, he played defensive end. In the last game that year, he was sent in as a substitute on the kickoff return team. The ball just happened to go to him and he took off running with it.
I ran over two tacklers before I realized what I was doing. I didn’t score or save the game, but I got a tremendous feeling carrying the ball. I was thrashing around, trying to run six ways at once. I loved it. I knew then that I wanted to run with the ball.
When he ran the ball it would take several players to take him down. Many times he would take three or four defenders into the end zone with him.
Csonka was heavily recruited by Clemson, Iowa, Vanderbilt, and Syracuse. He chose Syracuse, where he played middle linebacker in his first season before being switched to fullback from 1965–67
He established many of the school’s rushing records, including some previously held by Ernie Davis, Jim Nance, Floyd Little, and Jim Brown.
He was the Most Valuable Player in the East–West Shrine Game, the Hula Bowl, and the College All-Star Game. In 1989, he was enshrined in the College Football Hall of Fame.
"What makes Larry's accomplishments even more fantastic is that he gets so much of the yardage on his own, I think he is the most valuable player we have had in my 19 years at Syracuse"
Csonka was the #1 pick by the American Football League’s Miami Dolphins in the 1968 Common Draft, the eighth player and first running back drafted in the first round.
From 1970 – 1974 Csonka never missed a game, and led the Dolphins in rushing on into 1975. During this time he was one of the most feared runners in professional football
In 1972 the Dolphins became the only team since the AFL-NFL Merger to go undefeated. Csonka was an instrumental part, rushing for a career best 1,117 yards.