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This is the first law ever written on the subject in 1790 and signed by George Washington. It is significant because Washington was the president of the Constitutional Convention and many of the representatives and Senators were part of that convention:

United States Congress, “An act to establish an uniform Rule of Naturalization” (March 26, 1790).
Be it enacted by the Senate and House of Representatives of the United States of America, in Congress assembled, That any Alien being a free white person, who shall have resided within the limits and under the jurisdiction of the United States for the term of two years, may be admitted to become a citizen thereof on application to any common law Court of record in any one of the States wherein he shall have resided for the term of one year at least, and making proof to the satisfaction of such Court that he is a person of good character, and taking the oath or affirmation prescribed by law to support the Constitution of the United States, which Oath or Affirmation such Court shall administer, and the Clerk of such Court shall record such Application, and the proceedings thereon; and thereupon such person shall be considered as a Citizen of the United States. And the children of such person so naturalized, dwelling within the United States, being under the age of twenty one years at the time of such naturalization, shall also be considered as citizens of the United States. And the children of citizens of the United States that may be born beyond Sea, or out of the limits of the United States, shall be considered as natural born Citizens: Provided, that the right of citizenship shall not descend to persons whose fathers have never been resident in the United States: Provided also, that no person heretofore proscribed by any States, shall be admitted a citizen as aforesaid, except by an Act of the Legislature of the State in which such person was proscribed. http://www.indiana.edu/~kdhist/H105-documents-web/week08/naturalization1790.html

I've got the law saved someplace, and I'll get to it later, but in the meantime, here is the current method for getting an overseas birth certificate for your child born overseas so that they are AT BIRTH US Citizens:

Birth of U.S. Citizens Abroad
A child born abroad to a U.S. citizen parent or parents may acquire U.S. citizenship at birth if certain statutory requirements are met. The child’s parents should contact the nearest U.S. embassy or consulate to apply for a Consular Report of Birth Abroad of a Citizen of the United States of America (CRBA) to document that the child is a U.S. citizen. If the U.S. embassy or consulate determines that the child acquired U.S. citizenship at birth, a consular officer will approve the CRBA application and the Department of State will issue a CRBA, also called a Form FS-240, in the child’s name. http://travel.state.gov/content/passports/english/abroad/events-and-records/birth.html