Chemutai's winning time of 9:01.45 was also Uganda's National Record, and she also became the first East African woman to win the Olympics gold medal in the steeplechase since the event was added to the Summer Games programme in Beijing 2008.
Disgraced Bahraini Agnes Jebet won the gold in the 2016 Olympics but has since been banned from running for the use of performance enhancing drugs.
Frerichs clocked a season's best 9:04.79 while Kiyeng settled third in 9:05.39.
World record holder Beatrice Chepkoech, who has struggled with hamstring and tendon injuries this season, was seventh in 9:16.33 while Wilfred Mutile Yavi (9:19.74), the Kenyan-turned Bahraini, was 10th despite starting the race as one of the favourites.
Chemutai finished fourth in the 2019 World Championships won by Chepkoech.