In a novel analysis, we show that arbitrarily many Arbiter PUFs can be combined into a stable XOR Arbiter PUF. To the best of our knowledge, this design cannot be modeled by any known oracle access attack in polynomial time. Using majority vote of Arbiter Chain responses, our analysis shows that with a polynomial number of votes the XOR Arbiter PUF stability of almost all challenges can be boosted exponentially close to 1; that is, the stability gain through majority voting can exceed the stability loss introduced by large XORs for a feasible number of votes. Hence, our proposal enables the designer to increase the attacker's effort exponentially while still maintaining polynomial design effort for all known oracle access modeling attacks. This is the first result that relates PUF design to this traditional cryptographic design principle.