The Clintons bought the property next to their Chappaqua house and built or are building (without proper permits) a house on that property. I imagine the plan is to have Chelsea and her family move to Chappaqua and run for that Westchester seat.
I think the current office holder is Nita Lowry who had planned to run for the Senate seat of Daniel Patrick Moynihan before then FLOTUS Clinton decided she was going to move to NY and run for that seat, at which time Lowry stepped aside. When Lowry decides (or is told to) retire, Chelsea will likely run for her seat.
I think she died a few weeks ago.
Chelsea's odds of running successfully are between zero and minus infinity.
I totally believe that Freepers are not the only adult citizens to be absolutely and permanent enemies of Dynasties, no matter what the name. Those days are permanently over.
Good luck to the Clinton Criminal mini fat cow!