Her family owns an international shipping business that in the past has had some shady business practices such as flying under the flag of Liberia due to it's easier labor rules. Ms Chao was also the deputy secretary of transportation under GHW Bush though not much has come up from that time period.
And Matthew Yglesias at Vox says that while it's a reasonable choice given her experience, it is hyper partisan because of who her huband happens to be.
Henry Grabar at Slate has a few positive notes...
As far as transportation goes, Chao has had a fairly open mind. She acknowledged decades ago that the major era of highway construction was over and should give way to one focused on solving traffic congestion. In George H.W. Bush’s Department of Transportation, she helped fund an early iteration of GPS in Los Angeles. And as secretary of labor under George W. Bush, she praised the potential of public transit. “Coordinated transportation is one of the most important, and perhaps least appreciated, components of a transition from a life of unemployment and dependency for Americans to one of employment and productivity,” she said at a luncheon in 2004.She's also been a fellow at a number of conservative think tanks. Places like The Heritage Foundation and the Hudson Institute. She also has ties to big banks, was on the board at News Corp (Wall Street Journal) and organizations like the United Way where she was CEO and the director of the Peace Corps.
The Peace Corps stint was the most interesting to me because of the specific focus of her time in the Baltic States. Given the Brexit vote and now Trump's election and nationalist sentiments in greater Europe, it seems we are getting closer to a weakening of Europe and its ability to defend against Russia, which coincidentally has its eye on the Baltic states.
She established the first Peace Corps program in the Baltic nations of Latvia, Lithuania, Estonia, and the newly independent states of the former Soviet Union.According to CityLab, she's always wanted to be the Secretary of Transportation.
According to a 2001 Newsday article, Chao had mixed feelings about taking the cabinet post for the Department of Labor—which Chao later called “the most partisan of all the departments”—when President Bush initially asked her; she apparently had her “heart … set on leading the Department of Transportation.” Now she’ll get her shot.When she was at the Heritage Foundation she focused on writing about things like pensions. She's not a fan of largess in post retirement benefits and notes that unfunded obligations could be trouble for government agencies in the future. I imagine transit unions aren't fans of this stance.
She is also against Buy America provisions which affect procurement of vehicles for High Speed Rail in California or regular buses and trains.
The "Buy America" provision ("Dig a moat around America") in the stimulus package did more than squander America's credibility on international trade. It also created bureaucratic hoops that will slow down spending the stimulus funds on projects that are supposed to energize our economy.In a letter from the Congressional Record in 2003 to Representative Paul Sarbanes, Washington Metro's Lawrence Drake complained that then Secretary Chao was blocking commuter benefits for federal employees at the Labor Department. It seems the Labor Department under Chao wanted to use the increase from a $65 transit benefit to a $100 transit benefit as a bargaining chip in negotiations with workers. DC's Eleanor Holmes Norton said at one point during a protest "Who ever heard of the notion that the union has to negotiate for things they are entitled to under the law?"
This was all I could find for the moment, but I'm sure we'll hear more in the coming days as more people have time to do deeper research. Unfortunately the internet wasn't much of a thing during her first stint in the Transportation department.