Major cloud operators offer machine learning (ML) as a service, enabling customers who have the data but not ML expertise or infrastructure to train predictive models on this data. Existing ML-as-a-service platforms require users to reveal all training data to the service operator. We design, implement, and evaluate Chiron, a system for privacy-preserving machine learning as a service. First, Chiron conceals the training data from the service operator. Second, in keeping with how many existing ML-as-a-service platforms work, Chiron reveals neither the training algorithm nor the model structure to the user, providing only black-box access to the trained model. Chiron is implemented using SGX enclaves, but SGX alone does not achieve the dual goals of data privacy and model confidentiality. Chiron runs the standard ML training toolchain (including the popular Theano framework and C compiler) in an enclave, but the untrusted model-creation code from the service operator is further confined in a Ryoan sandbox to prevent it from leaking the training data outside the enclave. To support distributed training, Chiron executes multiple concurrent enclaves that exchange model parameters via a parameter server. We evaluate Chiron on popular deep learning models, focusing on benchmark image classification tasks such as CIFAR and ImageNet, and show that its training performance and accuracy of the resulting models are practical for common uses of ML-as-a-service.