After all, she was George W. Bush's labor secretary for two terms -- the longest-serving member of his Cabinet and the first female Asian-American in any presidential cabinet in US history. She is now President Donald Trump's transportation secretary and one of four women in his Cabinet.
But spending time with Chao in her office, I was immediately struck by something I did not expect -- how candid she is about her vulnerabilities and anxiety, especially about when she was a young Chinese immigrant.
"I remember how tough it was to try to learn a new culture, a new language and just to adapt to, like, ordinary daily stuff like the food. Like, most Chinese don't eat meat between breads," she told me with a laugh.
Eight-year-old Chao started her journey to America on an overnight train in Taiwan with her mother and two sisters in 1961. They then boarded a cargo ship to cross the Pacific Ocean to California before finally reaching their destination: New York.
"As an adult looking back and seeing my mother who was only like 27, you know how frightening it must have been as the only woman aboard this cargo ship with three young girls? I mean, that's pretty rough," she said.
In our nearly hour-long interview, Chao opened up about her struggles to adapt to a new country, her rise to power and her regrets about sacrifices she made along the way.
A tough transition for young Chao
Chao, her mother and sisters joined her father, who had come to the US three years earlier and lived in a one-bedroom apartment in Queens, New York.
"Those initial years were very hard," Chao said -- especially when she was first trying to learn English.
"The kids were mean to me," she recalled in a matter-of-fact tone that usually only comes with years of distance.
Her parents helped a lot, she said, providing "such a loving and secure" environment for her despite their own adversities and adjustment issues.
Chao's father eventually did very well in America, becoming a wealthy shipping magnate.
She said she felt a lot of pressure to succeed, noting that in Asian culture, the first-born child is expected to "take care of the rest of the children, my siblings."
"I was really scared that I would not be able to catch on, latch on to mainstream America. I wouldn't be able to find a job. I couldn't -- I couldn't make anything of myself. I'd be a disgrace to my family," she said.
No proms. No dates.
She was hardly a disgrace. Chao excelled academically and was accepted to Mount Holyoke, a women's college.
"We thought that that was the best place for, you know, a young girl to be. Little did I know then there would be, like, weekend dating situations," Chao said.
"I never dated in my whole entire life. I never went to my senior prom, never went to my junior prom," she revealed.
Although she clearly wasn't looking for sympathy, I told Chao that made me sad.
"That's OK," she reassured me, "I'm not. Nobody asked."
"I didn't understand the significance of it," she explained. "I didn't understand popular culture. I never listened to music because I didn't -- because, No. 1, I was too busy studying," she said.
That paid off. After college, Chao attended Harvard Business School to pursue a career in banking until she got a White House fellowship during the Reagan administration.
She said she was doing research for Republican President Ronald Reagan's speeches and "the bell went off, 'ding, ding, ding, ding!'"
"I was going, hey, I believe in all this stuff. I'm actually a Republican," she remembers.
Chao, 64, steadily climbed the GOP ranks with an appointment to the Maritime Commission, then deputy transportation secretary and eventually Peace Corps director. After Bill Clinton won the White House, she left government and became president of The United Way. It was around that time she met her husband, Sen. Mitch McConnell, who is now the Senate majority leader.
Her 'low-maintenance husband'
Chao scoffs at the idea of being one half of the ultimate power couple, noting rightly that these days there are a lot of power couples because there are so many more women in positions of power.
Chao played a significant role in her husband's 2014 reelection bid -- especially in helping him appeal to female voters as he competed against a female Democratic challenger, Alison Lundergen Grimes.
She is still eager to humanize her husband, who is known much more for his sharp political skills than a warm, fuzzy demeanor.
"This is really important. You've gotta leave this in," she says, looking directly into the television camera lens. "I call him my low-maintenance husband. He does his own laundry and he cooks."
"He does mine too sometimes," she said, referring to the laundry. "He's really good," she added about his cooking. "And he's really considerate," she continued, "and he's really very thoughtful. So, life with him, you know, is very easy that way."
A friend who set the couple up described Chao years later as a "tiger wife."
"At the time he made his remark, Amy Chua had her book about Tiger Moms. So I think he was trying to say that ... I am an incredibly loving, loyal wife and asset to my husband," she explained.
Chao brought up an article she once read that claimed that she keeps files on her husband's donors and supporters. She said the story was wrong -- but not why you may think.
"I didn't take notes. It was all up here," she said, her finger on her temple and a devilish look in her eyes.
"I have an incredible memory. It's just one of, you know, life's blessings. If I met you 24 years ago, I can remember the place, the time, the circumstances," Chao said -- a great asset in politics.
"It's proven to be pretty helpful," she agreed.
Her mother passed away, but her 90-year-old father still works and is her biggest cheerleader. He was there earlier this year when she was sworn in as transportation secretary.
As we looked at a photograph from that day, Chao remembered it was "January 31, 2017, at 5:30 p.m."
"I told you I have a good memory," she laughed.
Her candid regret: No children
Chao displays other photos in her office of her large family -- sisters, nieces and nephews.
She is very family-oriented but never had children of her own, and in a painfully candid moment during our discussion, she revealed that's a regret.
"I try not to have too many regrets. But I will say to young women, you know, when in my generation, we were taught that we can have it all. And so it was thought, well, you have a career. And then you would, you know, have your family and, well, there'd be no problem. Well, it doesn't work like that," she said, growing emotional.
"So I try to counsel young women that they will have to be, regardless as to whether they want it or not, there are tradeoffs and sacrifices in life. And it's important to know when those points occur because it would be a regret if you didn't know you were making that tradeoff and it happened. And there was no chance to go back."
Did she know she was making that tradeoff, I asked?
"No. I didn't," she replied, trying to hold back tears.
It was an unexpectedly raw moment with Chao that so many women can relate to. It resonated with me in a big way because I almost made the same "tradeoff," as she called it. I did not start trying to have a baby until I was in my late 30s, and it was almost too late. After years of fertility treatments, I finally got pregnant with my son, whom I call my miracle baby.
Because of my experience, I too tell young women that if they think they want children, it is important not to take that for granted. Watch the clock, because it matters.
Chao: A role model for many who didn't have one herself
Chao may not have her own kids, but there are scores of Asian-Americans who look to her for inspiration. Often, Chinese-American families meet her at airports just to say hi.
"Oh, my gosh. I mean, I would go to events. And they would show up. Asian-American families will show up everywhere. And there would be like, there'd be like an instant bond."
As transportation secretary, Chao oversees almost 60,000 employees and a slew of agencies, including the FAA. She says she tries to mentor young people who work for her -- but also surprised me by saying that role models are overrated.
"I'm gonna say something that seems a bit strange. But I want it to be encouraging. I didn't have a lot of role models. But that didn't hurt me. And so for young people, young women, I wanted to give them strength and hope and confidence," she declared.
"Just because there are no role models doesn't mean that you can't be the future role model that you now seek. So our country is so full of opportunities. And, you know, even if you don't have a role model, it's OK. Just pursue your life's passion. Do what you really love, and the way will unfold."