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The Loretto Chapel in Santa Fe, New Mexico is the correct answer. 

As the Loretto Chapel neared completion in 1873, the builders discovered a flaw in their plan to provide access to the choir loft, some twenty-two feet above the chapel floor. The sisters refused to allow a ladder to be built but there was no room for a staircase. As legend has it, a special novena to St. Joseph, patron saint of carpenters, was held. Soon a man appeared, looking for work and was contracted to build the staircase. Following months of work the staircase was completed but the man disappeared without being paid for his work. The unusual design perplexed engineers today. The staircase has two 360 degree turns, has no visible means of support and was built using only wooden pegs.

The above was copied from Landmark Details.