Conformal prediction is a popular paradigm for providing rigorous uncertainty quantification that can be applied to already trained models. We present an extension of conformal prediction to federated learning. The main challenge is data heterogeneity across the clients, which violates the fundamental tenet of \emph{exchangeability} required for conformal prediction. Instead, we propose a weaker notion of \emph{partial exchangeability} which is better suited to the FL setting, and use it to develop the Federated Conformal Prediction (FCP) framework. We show FCP enjoys rigorous theoretical guarantees as well as excellent empirical performance on several computer vision and medical imaging datasets. Our results demonstrate a practical approach to incorporating meaningful uncertainty quantification in distributed and heterogeneous environments.