What is the ruling on marrying a non-Muslim American woman in Islam?

It is permissible to marry an American woman if she is a chaste woman of the People of the Book, according to the Almighty's saying: (And [lawful in marriage are] the chaste women from among the believers and the chaste women from among those who were given the Scripture before you). But if she is not of the People of the Book or is not chaste, then it is not permissible to marry her, according to the Almighty's saying: (And do not marry polytheistic women until they believe). And a believing woman is better than a polytheistic woman or a woman of the People of the Book.