Over the past five years, LIGO and Virgo have published 50 detections of gravitational waves from compact binary coalescences. To infer the system parameters, an iterative algorithm such as Markov Chain Monte Carlo is used with Bayes' theorem to obtain posterior samples---by repeatedly generating waveforms and comparing to measured strain data. Although this produces accurate results, faster methods would be desirable to address the growing rate of detections and the need for rapid and accurate alerts for multi-messenger followup. In this work, we describe the use of simulation-based inference with deep neural networks to learn an inverse model for the parameters given the strain. The strategy is to use a normalizing flow to define a conditional density estimator, and train it to approximate the Bayesian posterior. Training requires simulated strain data, never any posterior samples or likelihood evaluations. The normalizing flow then enables fast sampling and density estimation for any strain data consistent with the training distribution. We demonstrate these methods by performing inference in seconds on the first gravitational-wave detection, GW150914.