Doing so is called "birth tourism." Saipan is a U.S. territory and is only a 4-5 hour flight from China. Excerpts:
"The Northern Marianas, an island chain that includes Saipan, is the only U.S. soil that Chinese can visit without a visa, after a change in immigration policy in 2009 allowed Chinese and Russian tourists visa-free entry for up to 45 days."
"The number of Chinese visitors has risen substantially since 2009 and now represents 36% of tourists to the island"
"The number of American babies born here to Chinese women who entered as tourists also climbed—to 472 last year from eight in 2009—according to the Northern Marianas government. Last year, for the first time, more Chinese tourists gave birth here than Americans."
"Chinese travel businesses offer competing packages to help Chinese mothers reach U.S. soil and provide them with lodging, hospital care and domestic help.
There is nothing illegal about birth tourism, provided the visitor has the funds to pay for required medical procedures and doesn’t intend to overstay"
"In China, websites advertising birth-tourism packages abound, with names such as GlobalBaby8.com, promising luxurious birth vacations to Saipan. The Chinese translator whose wife gave birth on Saipan said total costs can exceed $50,000.
“Everyone is feeling unsafe in China,” the father said, citing among other things the political crackdown under President Xi Jinping. “We will do anything for our kids.” The father still lives on Saipan with his wife and children, and fears they will be deported."
"Doctors and administrators said the surge in the number of Chinese mothers is overwhelming health facilities. “It’s a strain for the community,” said Esther Muna, CEO of government health provider Commonwealth Healthcare Corporation, which runs the hospital."