Ultimately, it is the candidate's choice on whether he or she will run for office. But, if Chelsea Clinton decides that she wants to run for a public office, then she absolutely should go and do it. I think she would be a great role model and follow very well in her parent's footsteps.
Chelsea Clinton has grown up in politics. Being the daughter of a former President and a Secretary of State she has a strong understanding of the operation of the federal government. Her family has a long tradition of public and community service. Chelsea would be a asset as a member of Congress from whatever state she is a resident of.
If Chelsea Clinton wants to run for public office and is serious about it, than why not? Anyone who wishes to run for public office should give it a go. That does not mean everyone will automatically get the position, just gives us citizens a larger variety of people to choose from.
Anyone who wants to run for office should give it a go. They may not be someone we like, or someone we want actually in office, but that is why we having a voting system. If a person feels they have something worthwhile, they should run for office, just not assume they will get it.