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    If your parent/parents served in the military, and you were born overseas, how could you acquire your birth certificate?

    Birth on US Military Base or Facility

    People born on a United States military facility outside of the United States should contact:

      American Citizens Born Abroad
    Department of State
    Correspondence Branch
    Suite 510
    1111 19th Street NW
    Washington, DC 20522

    People born on United States military facilities within a US State should contact the State office of Vital Records for the state the facility is in.

    You could also request your birth certificate from your sponsor’s medical record.

    Further information:

    This is the section of US Law that defines "Citizen at Birth", which is currently the legal definition of what "natural-born citizen" means:

    8 U.S. Code § 1401 - Nationals and citizens of United States at birth

    A person needs to satisfy only one of the conditions listed there to be considered a citizen at birth.

    Note that US Military bases are NOT considered US territory, though US Embassies (but not Consulates) ARE.  

    The Panama Canal Zone was explicitly included (by a US Law passed by Congress) to be "sovereign US soil".

    To answer the question: being born on a foreign US military base is no different than being born in a foreign country, for determination of US Citizenship at Birth. Neither qualify.  It would depend on the person's parents to determine eligibility for Citizenship at Birth.