Long Short-Term Memory (LSTM) networks offer unprecedented accuracy for prediction in ungauged basins. We trained and tested an LSTM on the CAMELS basins (approximately 30 years of daily rainfall/runoff data from 531 catchments in the US of sizes ranging from 4 km² to 2,000 km²) using k-fold validation, so that predictions were made in basins that supplied no training data. This effectively `ungauged' model was benchmarked over a 15-year validation period against the Sacramento Soil Moisture Accounting (SAC-SMA) model and also against the NOAA National Water Model reanalysis. SAC-SMA was calibrated separately for each basin using 15 years of daily data (i.e., this is a `gauged' model). The out-of-sample LSTM had higher median Nash-Sutcliffe Efficiencies across the 531 basins (0.69) than either the calibrated SAC-SMA (0.64) or the National Water Model (0.58). We outline several future research directions that would help develop this technology into a comprehensive regional hydrology model.