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The Chief Justice is the Supreme Overlord of the entire Judicial Branch, not just the court itself. A figure head but has some other duties besides the Supreme Court.

http://en.wikipedia.org/wiki/Chief_Justice_of_the_United_States

Duties

In addition to the duties of the Associate Justices, the Chief Justice has the following duties:

If the Chief Justice is in the majority on a Supreme Court case, he or she may decide to write the Opinion of the Court, or may assign it to an associate justice of his or her choice.

Presides when the Senate tries impeachments of the President of the United States

Two Chief Justices, Salmon P. Chase and William Rehnquist, have had the duty of presiding over Presidential impeachments and trials--Chase in 1868 over the proceedings of President Andrew Johnson and Rehnquist in 1999 over the proceeding against Bill Clinton.

Presides over the impeachment trial of the Vice President if the Vice President is serving as Acting President (not a Constitutional responsibility but a rule of the Senate).

Officiates at the inauguration of the President of the United States. This is a traditional, not a constitutional, responsibility of the Chief Justice. All federal and state judges, as well as notaries public, are empowered by law to administer oaths and affirmations.

Serves as the Chancellor of the Smithsonian Institution.

Serves as the head of the Judicial Conference of the United States, the chief administrative body of the U.S. federal courts.

The Judicial Conference is empowered by the Rules Enabling Act to promulgate rules to ensure the smooth operation of the federal courts. Major portions of the Federal Rules of Civil Procedure and Evidence have been adopted by most state legislatures and are considered canonical by American law schools.