We introduce a new portfolio credit risk model based on Restricted Boltzmann Machines (RBMs), which are stochastic neural networks capable of universal approximation of loss distributions. We test the model on an empirical dataset of default probabilities of 1'012 US companies and we show that it outperforms commonly used parametric factor copula models -- such as the Gaussian or the t factor copula models -- across several credit risk management tasks. In particular, the model leads to better fits for the empirical loss distribution and more accurate risk measure estimations. We introduce an importance sampling procedure which allows risk measures to be estimated at high confidence levels in a computationally efficient way and which is a substantial improvement over the Monte Carlo techniques currently available for copula models. Furthermore, the statistical factors extracted by the model admit an interpretation in terms of the underlying portfolio sector structure and provide practitioners with quantitative tools for the management of concentration risk. Finally, we show how to use the model for stress testing by estimating stressed risk measures (e.g. stressed VaR) under various macroeconomic stress test scenarios, such as those specified by the FRB's Dodd-Frank Act stress test.