China’s biggest bank, the Industrial and Commercial Bank of China, agreed Friday to pay $100 million to take control of the U.S. unit of the Bank of East Asia, the Wall Street Journal reports.

The Journal said the move would mark the first takeover of a U.S.-based bank by a Chinese state-owned lender, and could mark “the start of big expansions by Chinese financial institutions in the world’s largest economy.”

That may well be true. Even so, you’d have to say the Chinese have their work cut out for them with the Bank of East Asia.

The bank does have a location in the heart of New York City’s Chinatown neighborhood that has proved adept at gathering deposits. The bank had $425 million of deposits as of September, according to regulatory filings. That’s important because deposits can be a cheap way of raising funds.

But the Bank of East Asia’s deposit-raising success hasn’t been showing up on the bottom line. The bank’s U.S. unit made $2 million in the first nine months of 2010 — but lost money in each of the previous three years.

All told, Bank of East Asia NA has frittered away $41 million since 2007, while its loan book — heavily concentrated in real estate — has shrunk by 6% over that span, according to filings with the Federal Financial Institutions Examination Council.

For all of China’s posturing about the irresponsibility of the U.S. financial sector over the past decade or so, Bank of East Asia sounds like nothing so much as a miniature version of the sagging banks that have been littering the U.S. economic landscape.

Of course, the Chinese have some money and probably aren’t going to be too worried about a few million in losses here and there. It’s often said that the Chinese government, which owns 70% of ICBC, makes economic decisions based on an expansive, long term view of strategic interests, rather than focusing on the here-and-now view that is so prevalent in the U.S.

Good thing, too, given how ugly the here and now has looked lately with Bank of East Asia.