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 predict 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). Our results highlight how advances in the forecasting literature can be harnessed to improve causal inference in panel data settings.