Born in Houston, Texas, Gribble broke the world record in the 100-meter butterfly in 1983. He attended the University of Miami, where he swam for the Miami Hurricanes swimming and diving team in National Collegiate Athletic Association (NCAA) competition. While swimming for the Hurricanes, he won two NCAA titles, two gold medals in the 1982 World Aquatics Championships in Ecuador, and three gold medals at the 1983 Pan American Games. He was a member of the U.S. Olympic teams in 1980 and 1984.