It too has it's own little economy.
Niʻihau or Niihau (//; Hawaiian: [ˈniʔiˈhɔu]) is the seventh largest of the inhabited Hawaiian Islands in the U.S. state of Hawaiʻi, having an area of 69.5 square miles (180 km2). Niʻihau lies 17.5 miles (15.2 nmi; 28.2 km) southwest of Kauaʻi across the Kaulakahi Channel...] As of June 2009, the population was 130.
Elizabeth Sinclair purchased Niʻihau in 1864 from the Kingdom of Hawaii and private ownership passed on to her descendants, the Robinson family. During World War II, the island was the site of the Niʻihau Incident: A Japanese navy fighter pilot crashed on the island and terrorized its residents for a week after the attack on Pearl Harbor. The people of Niʻihau are known for their gemlike lei pūpū (shell lei) craftsmanship, and speak Hawaiian as a primary language. The island is generally off-limits to all but relatives of the island's owners, U.S. Navy personnel, government officials and invited guests, giving it the nickname "The Forbidden Isle." Beginning in 1987, a limited number of supervised activity tours and hunting safaris have opened to tourists. The island is currently managed by Bruce and Keith Robinson. (Courtesy of Wikipedia).
So...there you have it. Hawaii's smallest Island Economy. Limited Tourism is starting to happen and the United States Navy does have an installation on Niihau. For an interesting up date, see http://abcnews.go.com/GMA/WeekendWindow/hawaiis-forbidden-island-weekend-window-niihau/story?id=11767576&page=4