Live-cell imaging experiments have opened an exciting window into the behavior of living systems. While these experiments can produce rich data, the computational analysis of these datasets is challenging. Single-cell analysis requires that cells be accurately identified in each image and subsequently tracked over time. Increasingly, deep learning is being used to interpret microscopy image with single cell resolution. In this work, we apply deep learning to the problem of tracking single cells in live-cell imaging data. Using crowdsourcing and a human-in-the-loop approach to data annotation, we constructed a dataset of over 11,000 cell nuclear trajectories that includes lineage information. Using this dataset, we successfully trained a deep learning model to perform cell tracking within a linear programming framework. Benchmarking tests demonstrate that our method achieves state-of-the-art performance on the task of cell tracking with respect to multiple accuracy metrics. Further, we show that our deep learning-based method generalizes to perform cell tracking for both fluorescent and brightfield images of the cell cytoplasm, despite having never been trained those data types. This enables analysis of live-cell imaging data collected across imaging modalities. A persistent cloud deployment of our cell tracker is available at http://www.deepcell.org.