The American Samoa is an unincorporated territory of the United States. In 1901 the case Downes v Bidwell the Supreme Court held that the Citizenship Clause of the 14th Amendment does not extend birthright citizenship to U.S. nationals who are born in unincorporated territories. Here is a link to the court's decision- http://caselaw.findlaw.com/us-supreme-court/182/244.html