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I read somewhere that Hamilton himself thought that he was not eligible. I can't find that right now.

http://www.dorfonlaw.org/2008/02/alexander-hamilton-was-eligible-to-be.html
Snip:

Here I want to note a historical puzzle. It is frequently said that the "natural born Citizen" requirement was inserted in the text of the Constitution to prevent Alexander Hamilton---who was born in the West Indies---from becoming President. Some scholars note that this account is probably not true, but when they do so, they still tend to assume that Hamilton was not eligible to be President. For example, GW Law Prof Jonathan Turley says on his blog: "It is clear that the Framers considered natural born to refer to a birth on U.S. soil. Indeed, Alexander Hamilton was viewed as ineligible due to his birth in the West Indies."

Turley may well be right that Hamilton's contemporaries thought Hamilton ineligible for the Presidency. Reputable historians have said as much. But if so, Hamilton's contemporaries were surely wrong. It's true that Hamilton wasn't a "natural born Citizen," but the Constitution says that to become President one must be EITHER a "natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution . . . ." (boldface added). The boldface language was included because, at the time of the adoption of the Constitution, nobody who was old enough to be President had been born a citizen of the United States, there not having been a United States until July 4, 1776.