Final answer:
John Marshall's key accomplishment as Chief Justice was the establishment of the power of judicial review in the case of Marbury v. Madison, significantly strengthening the judiciary.
Step-by-step explanation:
John Marshall's most important accomplishment as Chief Justice of the Supreme Court was establishing the power of judicial review over state and federal laws. In the landmark case of Marbury v. Madison (1803), Marshall confirmed that the Supreme Court had the authority to review laws passed by Congress and actions taken by the President to determine if they were constitutional. This case set the precedent that solidified the role of the judiciary as an equal branch of government, capable of checking the powers of the other branches, which aligned with Marshall's intent to strengthen the federal government's role.