The primary role of the chief justice in the U.S. Supreme Court is to preside over court proceedings, ensure the efficient functioning of the judiciary, and lead the Court's deliberations. The chief justice has significant influence in deciding cases, especially as the deciding vote when the Court is evenly split. They also represent the judicial branch in official capacities, such as delivering the annual report on the state of the judiciary to Congress. Furthermore, the chief justice plays a crucial role in guiding judicial appointments and leading discussions about case prioritization.