We introduce “Natural” differential privacy (NDP)—which utilizes features of existing hardware architecture to implement differentially private computations. We show that NDP both guarantees strong bounds on privacy loss and constitutes a practical exception to no-free-lunch theorems on privacy. We describe how NDP can be efficiently implemented and how it aligns with recognized privacy principles and frameworks. We discuss the importance of formal protection guarantees and the relationship between formal and substantive protections.