First-time Olympians Chen and Chang, who arrived in Paris having won three consecutive world titles, finished on 337.68 points.
Chen and Chang kicked off the competition with a back dive in the pike position to loud cheers from the fans, many of whom were dressed in China's team jacket and waving national flags.
"Today we performed normally but we have higher standards for ourselves when it comes to the scores. We need to keep working at it," Chang, who looked emotional after winning her first Olympic gold medal, told reporters.
Americans Sarah Bacon and Kassidy Cook, who performed the same routines as Chen and Chang, gave the Chinese duo a scare after scoring equal points in the second round.
The Americans fell short in following dives, however, and took silver with 314.64 points.
"I don't think we had our all time best performance out there today, but we had a really solid performance and it's something that I'm very proud of," a grinning Kassidy said. "I'm very pleased with the silver medal."
"I think following the Chinese is a big responsibility almost," she said. "The Chinese hardly ever mess up but they kind of set the tone for the competition and pushed me and Sarah to put together five solid dives."
China have now won six Olympic titles in a row in the event, which was introduced into the Games programme in 2000.
Spectators at the Olympic Aquatics Centre, a new venue built for the Games in Saint-Denis, north of Paris, filled up the bulk of the seats to create a festive atmosphere.
Many were draped in national flags and cheered as the divers performed twists and somersaults before the final plunge.
China's Guo Jingjing, a four-times Olympic gold medallist in the 3m springboard event, refereed Saturday's competition and was given a loud cheer when she was introduced on the screen.
Chen, the world number one, is set to compete with her best friend Chang in the 3m individual event.
Yasmin Harper and Scarlett Mew Jenson took bronze, Britain's first medal in Paris.