Anyone (U.S. citizen, non-criminal) should be able to run. Not saying anything about her qualifications etc. But if we're to have a government by, for and of the people, then any of our "people" should be able to run after meeting whatever pre-requisites exist. Chelsea Clinton has had enough exposure to public life that she may be wary of entering the political fray, but if she wants to, she should go for it.
I think anyone that wants to, should be able to run for office. Chelse Clinton grew up in politics so she knows exactly how they work. She has second hand experience watching her mother and father while they were in offices. Everyone may not agree with her or any candidate on all issues, but I think anyone should have the right to run for an elected office.
Although her mother's historic achievement (winning the popular vote but losing the electoral college) paved the way for a new era in politics, Chelsea Clinton should not run for office. Throughout Hillary's campaign, one of the biggest reasons that voters expressed dissatisfaction with her (aside from the email scandal) was that Hillary would continue a political dynasty that began with her husband's presidency. Voters of all stripes, from independent to far-right conservative, believed that the time has come for a truly dramatic shift in the shape of our government, one that sweeps out the old and brings in the new. If Chelsea Clinton ran for office, this would continue the Clintons' deep involvement in politics, but not make voters feel that a change is being made. Chelsea Clinton is wise to continue her involvement in the Clinton Foundation and remain as removed as possible from her parents' political ambitions.
How does Chelsea Clinton manage to afford her $10 million condo? What has she done that would enable her to pay for that? Rather, she got the money for the condo from the Clinton Foundation. The Clinton Foundation funneled money from politicians around the world in a pay-for-play scheme. We do not need one more corrupt politician.