We present a data-driven framework called generative adversarial privacy (GAP). Inspired by recent advancements in generative adversarial networks (GANs), GAP allows the data holder to learn the privatization mechanism directly from the data. Under GAP, finding the optimal privacy mechanism is formulated as a constrained minimax game between a privatizer and an adversary. We show that for appropriately chosen adversarial loss functions, GAP provides privacy guarantees against strong information-theoretic adversaries. We also evaluate the performance of GAP on multi-dimensional Gaussian mixture models and the GENKI face database.