The most famous first daughter in recent memory is warming up for a long day on the campaign trail. Fielding students' health policy questions for a full hour in Hershey, Pa., she allows, just briefly, a peek into her own life, telling how she once moved into her sick grandmother's hospital room to help with the paperwork. Then she catches herself: "My grandmother would be mortified that I'm sharing this with you all!" she says.

Getting personal doesn't come easy for this Clinton. Twice in past weeks she has been asked about her mother's reaction to the Monica Lewinsky scandal that threatened to sink her father's Presidency. Both times Chelsea, 28, who takes questions from the crowd but not from reporters, was firm: "I'm sure there are things that are personal to your family that you don't think are anyone's business either," she shot back to one student. Pundits have debated whether the question and response were appropriate, but one young political junkie has no doubts. "It's never appropriate to ask a child about the marital infidelities of her parent," says Bucknell junior Lee Markinson, 21, a Republican, "no matter the arena or how old the child."

In fact, "I feel so old" is one of Chelsea's standard lines as she strides through 12-hour days in jeans and patent-leather stilettos. Since December, Clinton, who is on leave from her job at a Manhattan hedge fund, has logged visits to 100 college campuses—flying commercial with no Secret Service. Her boyfriend, banker Marc Mezvinsky, 30, occasionally meets up with her on the road and has given her a Yorkshire terrier named Soren, after Danish philosopher Søren Kierkegaard.

Asked if she would ever add a political job to her résumé, Chelsea says she's content with where she is—for now. "I have a boyfriend and a dog," she told a student she met recently, "and I still haven't figured out what I want to be when I grow up."