Noted for her fast start, she was the 1st leg runner in two US Olympic 4×100 Relay teams 1984–88, both teams winning the gold. At the 1984 Summer Olympics, in the individual 100 metres, Brown and American teammate Jeanette Bolden charged out to the lead, only to be overtaken by world record holder Evelyn Ashford, with Brown clearly taking the silver medal. Later, the U.S. relay team won the gold medal beating Canada by over a second, the greatest winning margin in the event's history. This was due to a very strong team which included all three U.S sprinters that made the 100 m final and Brown's superb start. The US were clear favourites as the GDR and USSR teams who would have provided stiff competition were absent due to the Eastern Bloc boycott. The team was never seriously challenged, leading from gun to tape and triumphing with a time of 41.65 seconds, one of the fastest times in history.
In 1987 Alice won 4×100 relay Gold at the World Championships Rome, Italy. A very strong and well-drilled team consisting ofDiane Williams, Florence Griffith-Joyner and Pam Marshall were favorite. They won their semi-final with a time over a second faster than the usually dominant GDR team. They went on to win the final from the GDR team, clocking a time of 41.58 CR, which was a U.S record at the time, and still ranks as one of the fastest times in history.
1988 Olympics
In the 1988 Seoul Olympic Games all nations were present for the first time since the Montréal games in 1976. In the final of the Women's 4×100 Relay all the strongest nations were present except for the Jamaicans who were non starters. Alice Brown once again led the United States challenge running the first leg. In a superb piece of relay running, she left the field trailing in her wake. By the time she handed over to Sheila Echols, she had caught and was passing the Bulgarian athlete in the next lane. Florence Griffith-Joyner took over and ran solidly, handed over to Evelyn Ashford, who in very impressive fashion made up three metres on Marlies Göhr and led the US team to victory by a clear metre. The winning time was down on the U.S record due to sloppy baton exchanges. It was superior basic speed and sheer talent that won the U.S their second consecutive gold in this event.