Born in Saint Michael, Thompson was educated in marketing and economics at the University of Texas, United States. A Junior World Record holder in 1994, he came close to winning an Olympic medal at the 1996 Summer Olympics in Atlanta, when he finished 4th in the 200 m final, which was won by Michael Johnson in a new World Record time.
Although with the top sprinters in the late 1990s, Thompson just failed to win any medals in major championships, finishing fourth in both the 100 m and 200 m at the 1999 World Championships. He finally managed to win a medal at the 2000 Summer Olympics in Sydney, Australia, finishing third behind Maurice Greene to become a national hero in Barbados. Thompson missed out on a second medal by again ending up in fourth place in the 200 m race.