Answer:
Unlike its requirement that the President be a "natural born" citizen, and the Senators and Representatives be at least "naturalized," the Constitution is silent on the citizenship and residency requirements for a Supreme Court Justice.
Naturalized citizens are eligible to serve on the Court. In order to become a naturalized citizen, a person must be at least 18 years old and must have been a permanent resident in the United States for at least five years, or for three years, if married to and continuously living with a spouse who's an American citizen. A person voluntarily serving in the US military is eligible to apply for citizenship after one year of service, or within six month of being honorably discharged.
Non-citizen residents of the United States are not legally eligible for a position on the Court.
For more information on the Supreme Court justice qualifications, see Related Questions, below.