Ms Chen, originally from Taiwan, and her Chinese husband, who is also born under the dragon sign, had planned a dragon baby since they got married eight years ago.
"There is a story from Taiwan that if a family has three dragons, the family will have extremely good fortune," she said.
Trust chairwoman Kylie Liu, 32, says cultural differences also made raising children here difficult for Chinese mothers.
"After a woman gives birth in China, we believe in having one month of confinement where she doesn't leave the house, and gets special food, drink and herbal remedies to repair her body," said Ms Liu.
"But here women are asked to leave the hospital after a few hours, and can go out with their babies the next day."
Ms Liu said many parents who planned to have Dragon-year babies had "traditional Chinese thinking" and often find themselves caught between the cultures of East and West.
"Our group is very much like the coffee group that Kiwi mothers have, but I guess what we talk about more is how to get the best out of the East and West on how we raise our child."
Associate Professor Elsie Ho, from the University of Auckland School of Population Health, said the desire and enthusiasm of Chinese parents to have Dragon-year babies were "very real" and countries with strong Chinese diaspora populations, including New Zealand, will see a sharp increase in Chinese babies born this year.
She said the impact would be more greatly felt in Auckland, where in a few years students would have "quite a few more Chinese classmates".
Statistics New Zealand analyst Anne Howard said it was too soon to see if there had been a surge of Asian births since the start of the Dragon year, as birth statistics are derived from birth registrations and not the date of birth.