Chief Justice

The official title of the presiding judge of the U.S. Supreme Court is chief justice of the United States, not chief justice of the Supreme Court. Capitalize as a title when it immediately precedes a personal name; otherwise lowercase, including appositives.

The chief justice heads the entire federal judiciary, not just the Supreme Court:

            Chief Justice John Roberts

            Associate Justice of the Supreme Court Ruth Bader Ginsburg

            Associate Justice Ginsburg

            the associate justice