Empirical scoring functions based on either molecular force fields or cheminformatics descriptors are widely used, in conjunction with molecular docking, during the early stages of drug discovery to predict potency and binding affinity of a drug-like molecule to a given target. These models require expert-level knowledge of physical chemistry and biology to be encoded as hand-tuned parameters or features rather than allowing the underlying model to select features in a data-driven procedure. Here, we develop a general 3-dimensional spatial convolution operation for learning atomic-level chemical interactions directly from atomic coordinates and demonstrate its application to structure-based bioactivity prediction. The atomic convolutional neural network is trained to predict the experimentally determined binding affinity of a protein-ligand complex by direct calculation of the energy associated with the complex, protein, and ligand given the crystal structure of the binding pose. Non-covalent interactions present in the complex that are absent in the protein-ligand sub-structures are identified and the model learns the interaction strength associated with these features. We test our model by predicting the binding free energy of a subset of protein-ligand complexes found in the PDBBind dataset and compare with state-of-the-art cheminformatics and machine learning-based approaches. We find that all methods achieve experimental accuracy and that atomic convolutional networks either outperform or perform competitively with the cheminformatics based methods. Unlike all previous protein-ligand prediction systems, atomic convolutional networks are end-to-end and fully-differentiable. They represent a new data-driven, physics-based deep learning model paradigm that offers a strong foundation for future improvements in structure-based bioactivity prediction.