CHICAGO—China's biggest bank signed an agreement that would make it the first Beijing-controlled financial institution to acquire retail bank branches in the U.S., though regulators could still block the deal.

Under the deal, Industrial & Commercial Bank of China Ltd., by some measures the world's largest bank, agreed to acquire a majority stake in Bank of East Asia Ltd.'s U.S. subsidiary. ICBC will pay $140 million for an 80% stake. Bank of East Asia, which is a publicly traded company based in Hong Kong, has a total of 13...