Is Cape Hatteras Lighthouse still in operation?

No, the Cape Hatteras lighthouse is not the oldest lighthouse anywhere, not in the state, not in the world, not in the country. The Cape Hatteras lighthouse is, though, the tallest lighthouse in the United States. Actually, it is the tallest lighthouse in North America. It is one of the tallest brick lighthouses in the world, at 193 feet tall. If it is the oldest anything, it is the oldest lighthouse in the town of Buxton, being the only lighthouse in the town of Buxton.