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A large-scale artificial neural network, a three-layer perceptron, is implemented using two phase-change memory (PCM) devices to encode the weight of each of 164,885 synapses. The PCM conductances are programmed using a crossbar-compatible pulse scheme, and the network is trained to recognize a 5000-example subset of the MNIST handwritten digit database, achieving 82.2% accuracy during training and 82.9% generalization accuracy on unseen test examples. A simulation of the network performance is developed that incorporates a statistical model of the PCM response, allowing quantitative estimation of the tolerance of the network to device variation, defects, and conductance response.