Yes, individuals born in St. Croix (which is part of the U.S. Virgin Islands) are automatic U.S. citizens at birth. This is governed by the 14th Amendment and specific federal statutes that grant birthright citizenship to those born in organized, incorporated U.S. territories. People born in St. Croix have the same rights as citizens born in the 50 states, including the right to a U.S. passport, the ability to move freely to the U.S. mainland, and the ability to serve in the military. The only significant difference is that, while living in the territory, residents cannot vote in U.S. presidential elections and do not have a voting representative in Congress. However, once a St. Croix-born citizen establishes residency in any of the 50 states, they gain full voting rights. They are considered "natural-born" citizens, making them eligible for any office, including the Presidency.