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A person born in the United States who is subject to the jurisdiction of the United States is a U.S. citizen at birth, to include a child born to a member of an Indian, Eskimo, Aleutian, or other aboriginal tribe. -Chapter 3 - U.S. Citizens at Birth (INA 301 and 309), US Customs and Immigration Policy Manual
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. -14th Amendment to US Constitution

The 14th Amendment goes on to say:

No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.