Tolliver was selected by the San Diego Chargers in the second round of the 1989 NFL Draft. The Chargers traded third, fourth, and seventh-round picks in exchange for the New York Giants' second-round pick in order to draft him. Tolliver was signed on July 31, 1989, after a short holdout. He was to compete with Mark Malone and David Archer for the starting job, a spot which eventually went to Jim McMahon after the Chargers traded for him. As the 1989 season began with McMahon as the helm, Tolliver was slated to play the second half of the final preseason game against the Phoenix Cardinals. After 13 completions in 23 attempts, Tolliver ran the ball late in the game and broke his collarbone, sidelining him for at least six weeks. After spending the first seven games on the injured reserve list, Tolliver was taken off the list and named the starter for the game against the Seattle Seahawks on October 29, replacing McMahon who had disappointed at quarterback. In Tolliver's first start, he played three quarters, throwing six completed passes in 17 attempts for 41 yards and throwing an interception in a 10–7 loss. Tolliver subsequently lost the starting job back to McMahon. However, in late November, Tolliver was given the starting job back, remaining the starting quarterback the rest of the season. Tolliver finished the season having played five games with 89 completions in 185 attempts, 1097 yards, five touchdowns, eight interceptions, and a 57.9 quarterback rating.