Treaties must comply with the Constitution. However, the treatymaking power of the U.S. Government is broader than the law making power of Congress. The Supreme Court ruled in Missouri v. Holland (1920) that pursuant to a treaty with Great Britain, the United States could regulate the hunting of migratory birds, even though Congress had no independent authority to pass such legislation.
Article VI, Clause 2: "This Constitution, and the laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the authority of the United States, shall be Supreme Law of the land; and the Judges in every state shall be bound thereby, any thing in the Constitution or Laws of any state to the contrary notwithstanding."