Montague Island lies in the Gulf of Alaska at the entrance to Prince William Sound, Alaska. The island has a land area of 790.88 km², making it the 26th largest island in the United States. As of the 2000 census, Montague did not have a permanent resident population, making it at that time the largest uninhabited island in the United States. Since then, the 2010 …Montague Island lies in the Gulf of Alaska at the entrance to Prince William Sound, Alaska. The island has a land area of 790.88 km², making it the 26th largest island in the United States. As of the 2000 census, Montague did not have a permanent resident population, making it at that time the largest uninhabited island in the United States. Since then, the 2010 abandonment of the United States Coast Guard station on Attu Island in the Aleutian Islands, which at 892.8 km² is larger than Montague Island, causes Attu to claim that title. Montague Island was named by Captain James Cook in honor of John Montagu, 4th Earl of Sandwich, one of his greatest supporters.