Also known as the Touro Tower, the Stone Tower, etc. It is one of the great mysteries of early America. It was possibly built by Benedict Arnold the first, governor of Rhode Island, in the 1670s. However, it could be much older. It bears similarity to various Norse round towers and churches, and could have once sported a conical roof and a 'skirt' area. It has astronomical oddities that would make it unlikely to be a simple windmill, and a "Norman estate" is mentioned in Verrazano's observations of the area, long before Arnold and his ilk.
We had a chance to check it out recently, and it is definitely odd. If it was 17th century architecture it was nearly unique. The large stones near the base of the pillars are bizarre and not exactly smart, unless they were originally underground, or if there were flying buttress-like attachments to the rest holding it up.
In some ways it is slipshod and uneven, and in others so precise and astronomically centered, that it is hard NOT to be suspicious that Viking mariners built it long before the arrival of the pilgrims. I am no expert, but I understand why this strange building is at the heart of so many bizarre theories.