We examine the use of deep learning (neural networks) to predict the movement of the S&P 500 Index using past returns of all the stocks in the index. Our analysis finds that the future direction of the S&P 500 index can be weakly predicted by the prior movements of the underlying stocks in the index. Decomposition of the prediction error indicates that most of the lack of predictability comes from randomness and only a little from nonstationarity. We believe this is the first test of S&P500 market efficiency that uses a very large information set, and it extends the domain of weak-form market efficiency tests.