This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP constructs the predictive set based on random samples from an estimated generative model. It is efficient and compatible with conditional generative models with either explicit or implicit density functions. We show that PCP guarantees correct marginal coverage with finite samples and give empirical evidence of conditional coverage. We study PCP on a variety of simulated and real datasets. Compared to existing conformal prediction methods, PCP provides sharper predictive sets.