When the credit crisis erupted a year ago, some Americans worried that China’s big banks might buy up capital-starved U.S. lenders. That hasn’t happened, but the Chinese are still coming.

Last month Beijing-based Industrial and Commercial Bank of China, the world’s largest bank by market capitalization, and Shenzhen-based China Merchants Bank, the country’s sixth-largest lender, opened branches in New York. It’s the first time Chinese banks have opened branches in New York since the 1991 passing of the Foreign Bank Supervision Enhancement Act, which required solid regulatory regimes in the banks’ home countries. Undeterred by the troubled U.S. economy, the ...