With COVID-19 affecting every country globally and changing everyday life, the ability to forecast the spread of the disease is more important than any previous epidemic. The conventional methods of disease-spread modeling, compartmental models, are based on the assumption of spatiotemporal homogeneity of the spread of the virus, which may cause forecasting to underperform, especially at high spatial resolutions. In this paper, we approach the forecasting task with an alternative technique—spatiotemporal machine learning. We present COVID-LSTM, a data-driven model based on a long short-term memory deep learning architecture for forecasting COVID-19 incidence at the county level in the USA. We use the weekly number of new positive cases as temporal input, and hand-engineered spatial features from Facebook movement and connectedness datasets to capture the spread of the disease in time and space. COVID-LSTM outperforms the COVID-19 Forecast Hub’s Ensemble model (COVIDhub-ensemble) on our 17-week evaluation period, making it the first model to be more accurate than the COVIDhub-ensemble over one or more forecast periods. Over the 4-week forecast horizon, our model is on average 50 cases per county more accurate than the COVIDhub-ensemble. We highlight that the underutilization of data-driven forecasting of disease spread prior to COVID-19 is likely due to the lack of sufficient data available for previous diseases, in addition to the recent advances in machine learning methods for spatiotemporal forecasting. We discuss the impediments to the wider uptake of data-driven forecasting, and whether it is likely that more deep learning-based models will be used in the future.