Drafted by the Atlanta Braves in the 8th round of the 1987 amateur draft, Hunter appeared in three World Series in 1991, 1992 and 1999 as a member of the Braves. Hunter hit a home run in Game 5 of the 1991 series in a 14–5 Braves victory over the Minnesota Twins. He hit a two-run home run in the first inning of the deciding game 7 of the 1991 National League Championship Series at Three Rivers Stadium vs the Pittsburgh Pirates; the Braves won the game 4–0, advancing to the 1991 World Series to face the Minnesota Twins.