Since Puerto Rico is part of the United States, then of course you do not need a passport.

I have a question of my own, which is probably even more silly, but I do not quite understand the distinction between "commonwealth" and "state." Puerto Rico makes quite a point of noting that THEY are a commonwealth rather than a state. However, Virginia definitely and I'm pretty sure Pennsylvania also are commonwealths, and yet they are also states just fine, indeed, some of the original states. So what's up with that?