The victory was a record fifth career Olympic gold medal for Chen, tying the mark set just two days earlier by team-mate Wu Minxia.
The Chinese triumphed despite a spirited challenge from Malaysia's Pandelela Rinong and Cheong Jun Hoong, who took silver.
Meaghan Benfeito and Roseline Filion of Canada, the bronze medallists in London, matched that finish in Rio.
The Chinese took a slim early lead and managed to hold on, finishing at 354.00 points, just 9.44 points clear of the Malaysians.
The victory by the reigning world champions extended what has so far been a dominating performance by the Chinese in Rio.
No team has yet swept all eight medal events in the diving well since the number of Olympic events was doubled at Sydney 2000 with the addition of 10m and 3m synchronised diving.
China has come close though, falling just one gold shy as hosts in 2008, and winning six of them in London four years ago.
It was a three-peat gold in the event for Chen, 23, who won with different partners in Beijing and London.
She also won the individual 10m platform in both of those Games but is not entered for Rio.