Final answer:
The Chief Justice presides over the Senate trial during the impeachment proceedings of a U.S. President to ensure impartiality and manage procedural matters.
Step-by-step explanation:
The duty of the Chief Justice of the Supreme Court in impeachment proceedings is specifically outlined for the case when a President of the United States is being tried. In such cases, the Constitution mandates that the Chief Justice preside over the Senate trial. This is to ensure the impartiality of the proceedings, as the Vice President—who is normally the presiding officer of the Senate—could potentially have a conflict of interest if the outcome would elevate them to the presidency. The Chief Justice's role is primarily to maintain order and provide rulings on procedural matters during the trial, not to determine the outcome of the impeachment.