Final answer:
Marbury v. Madison is the landmark case from 1803 that established the Supreme Court's power of judicial review.
Step-by-step explanation:
The landmark case from the year 1803 that established the Supreme Court's power of judicial review is Marbury v. Madison. In this case, Chief Justice John Marshall ruled that Marbury had the right to a legal remedy but also found that Congress's Judicial Act of 1789 was unconstitutional. This case established the principle of judicial review, giving the Supreme Court the power to review and potentially nullify the actions of Congress and the president.