Without an actual SAT score, it's too early to ask for chances.
That said, your PSAT score (which translates to a 2000 SAT) needs to be, at minimum, 100 points higher to be a viable applicant. See: The trodden path: Applying as a legacy - The Daily Princetonian
"A legacy applicant is now viewed, “first and foremost, on his or her academic performance,” Dean of Admission Janet Rapelye said in an e-mail, emphasizing that the size of the applicant pool forces her office to reject many students with outstanding credentials, whether these students are legacies or not.
Applicants who have “significant family ties to the University … are evaluated in the same rigorous review as every applicant,” Rapelye explained. “We assess the applicant and not the parent. In a small number of cases we do take into account the nature of a family’s ties to Princeton.”
The University has admitted between 34 and 47 percent of legacy applicants over the last 17 years, maintaining the proportion of the class made up of alumni children at a steady 10–15 percent, Rapelye said."