DOUGLAS GINSBURG, Federal Judge, U.S. Court of Appeals, D.C. Circuit:
The Chief Justice of the United States now is John G. Roberts, Jr.

The Constitution mentions the chief justice only once – and not in Article III which concerns the judiciary, but in Article I which concerns the Congress. It provides that, if the president of the United States is impeached by the house, then "the chief justice" shall preside over his trial in the Senate.
Congress created the titles of “Chief Justice of the United States” and “Associate Justice of the Supreme Court” a year after the Constitution was ratified. Like other federal judges, the chief justice is nominated by the president, approved by the Senate, and serves until death, resignation, or removal by impeachment.
The chief justice presides over the arguments before the Court, and chairs the conferences where the justices discuss the cases, but has one vote like every other justice. When voting with the majority, the chief justice may write the Court's opinion, or delegate that task to one of the associate justices.
“Ladies and gentlemen, it’s an honor to introduce the Chief Justice of the United States, John G. Roberts, Jr. who’ll administer the presidential oath of office.” “Please raise your right hand and repeat after me.” “I, Joseph Robinette Biden, Jr. do solemnly swear …” You may have watched the chief justice swear in a president during an inauguration, a tradition, not a legal requirement. Biden: “office of president of the United States …” “And will, to the best of my ability …”
Film footage: “Justice Groner of the court of appeals swears in Fred M. Vinson as the 13th chief justice of the Supreme Court.” The title, Chief Justice of the United States, reflects the chiefs’ role as the administrative head of the federal courts. If you have visited Washington D.C. you may be familiar with some of the chief justice’s other duties: He sits on the boards of the National Gallery of Art and the Hirshhorn Museum – and he serves as chancellor of the Smithsonian Institution.