"We talked about raising children in the public spotlight because she had done it with such grace and success," the former first lady told Barbara Walters in a 2003 interview. "She stressed how you could never let your child become kind of an object of all this public interest, because it would ruin them. You had to keep making sure they didn't feel entitled or indulged. And I took those lessons to heart."
Hollywood film director Harry Thomason — who is a close friend to the Clintons — said that during her father's presidency, Clinton kept a low profile.
"I don't think Chelsea is one of those people that she has ever wanted to be the center of attention," Thomason said. "We can all see that over the following years — she had plenty of chances to be the center of attention in the White House and in her college years, and she's just always chosen not to. I think that speaks well of the people who raised her."
Caputo agrees and thinks that the zone of privacy set up by her parents is one of the reasons Clinton is so grounded today.
"I think she is one of the most poised, elegant, grounded insightful intelligent young women I know," she said. "She has been able to live her life that has not been in the public eye but rather had her life have some kind of privacy and protection to it. That I think has enabled her to live this normal life that otherwise would have been very difficult to lead."
Clinton has kept out of politics until relatively recently. She gave her first political speech four years ago in support of Sen. John Kerry. Now she is a constant presence on the campaign trail.
"I think she's more vocal now because she has her own place in the world, and she's a highly successful businesswoman," Thomason said. "And I think she feels she can speak out and nobody thinks it's necessarily because she's been manipulated by the campaign or anything else."
It's clear she never expected to be as involved in her mother's presidential bid as she is now. Back in Iowa before the holidays, she told reporters she might spend her Christmas holiday doing a little campaigning. Instead, she hasn't had a day off in 22 days.
Her role is to parachute in to the places the senator and former president can't reach. With Illinois Sen. Barack Obama enormously popular among young people, Clinton is the one surrogate for her mother who can draw big crowds on college campuses.
But to some in the crowd, she could be the Clinton with the most political promise.
After a speech in Youngstown, Ohio, a voter asked her, "Are you sure you don't reconsider and run for office?" Clinton dismissed the question as mere "flattery," and told the voter that "my political aspirations stretch to having my mom be my president."
Caputo doesn't think that she is the political animal her parents are.
"I don't think she is at all, you know," Caputo said. "I think she's got her own life, she's pursuing her own career interests, which are outside of politics, and I think she's involved in this campaign because it's her mom and she deeply believes her mom would make a great president. And she wants to do everything she can to help her become president."
But with her genes, it's not entirely clear she will be able to resist the pull of politics.