While the Federal Reserve is a privately-owned institution (it is not a government agency* at all, contrary to popular belief,) the Chairman and Board of Governors get technically nominated by the president and confirmed by the senate every four years. I think Benny's current term is up in 2010.
* Wikipedia claims the Fed is a "quasi-public and quasi-private (government entity with private components)", but that's massively understating the fraud that is the "Federal Reserve."