Machine learning models benefit from large and diverse datasets. Using such datasets, however, often requires trusting a centralized data aggregator. For sensitive applications like healthcare and finance this is undesirable as it could compromise patient privacy or divulge trade secrets. Recent advances in secure and privacy-preserving computation, including trusted hardware enclaves and differential privacy, offer a way for mutually distrusting parties to efficiently train a machine learning model without revealing the training data. In this work, we introduce Myelin, a deep learning framework which combines these privacy-preservation primitives, and use it to establish a baseline level of performance for fully private machine learning.