Conducting causal inference with panel data is a core challenge in social science research. We adapt a deep neural architecture for time series forecasting (the N-BEATS algorithm) to more accurately impute the counterfactual evolution of a treated unit had treatment not occurred. Across a range of settings, the resulting estimator (``SyNBEATS'') significantly outperforms commonly employed methods (synthetic controls, two-way fixed effects), and attains comparable or more accurate performance compared to recently proposed methods (synthetic difference-in-differences, matrix completion). An implementation of this estimator is available for public use. Our results highlight how advances in the forecasting literature can be harnessed to improve causal inference in panel data settings.