Proudly Built in the USA—by the Chinese

Of the three companies profiled by CNBC for this series, China Construction America has been investing in the U.S. the longest: 28 years. It is also the only one of the three that is majority-owned by the Chinese government.

CCA has been in the U.S. so long that it has been the focus of two Harvard Business School studies. After first setting up shop in the U.S., CCA struggled for nearly a decade. Rather than focusing on its core strength of contract construction, executives tried their hand at real estate development and failed.

Current CEO Ning Yuan told CNBC, "We invested a lot in the first three years, and got into trouble. And in the next ten years, we tried to solve the problem. We worked very hard to solve that problem."

When Yuan took over 13 years ago, he refocused the company on contract construction. After building a factory for a fellow Chinese company, Heier Appliances, in South Carolina, Yuan learned the ins and outs of the South Carolina market. "We learned once we get into a new market, we should do everything step-by-step. Know the law system, know the code," he said. "Then gradually you can do your own business and become successful."

CCA began bidding on municipal projects and eventually went on to build half a dozen public schools in the state. The company's also been successful in New York, winning the $407 million contract for the rehabbing the Alexander Hamilton Bridge, and the $66 million Yankee Stadium Train Station.

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At its U.S.-based projects, all the labor is American. But at its multi-billion dollar Baha Mar project in the Bahamas, CCA flies in laborers from China.

While wining jobs at the state and municipal level, CCA has struggled to win any big federal projects. Yuan believes its failure to do so may be political in nature, because CCA is a foreign firm.

CCA is a wholly owned subsidiary of China Construction Engineering—famous for the Water Cube at the Beijing Olympics. Although its parent company is publicly traded on the Shanghai stock exchange, the majority of the shares are still owned by the Chinese government—a holdover from the days when the government controlled every company.

Government-owned firms face wide distrust in the U.S. Critics suggest they are given special advantages from the country's leadership, or at a minimum, very cheap financing from the country's banks, which are also government-controlled.

Yuan said of the financing allegation, "that is totally wrong." He said that even in China, CCA's parent company has to enter a competitive bidding process in order to get government work. When it comes to cheap financing, he says while the banks are still state -owned, they do want to be profitable. So he's paying the same interest rate as any other competitor in the market.

Emphasizing his sentiment by tapping his chest, he said, "I know from my heart we don't get any advantage."

—By CNBC's Michelle Caruso-Cabrera. Follow her on Twitter: @MCaruso_Cabrera