Biological networks are powerful tools for predicting undocumented relationships between molecules. The underlying principle is that existing interactions between molecules can be used to predict new interactions. Here we use this principle to suggest new protein-chemical interactions via the network derived from three-dimensional structures. For pairs of proteins sharing a common ligand, we use protein and chemical superimpositions combined with fast structural compatibility screens to predict whether additional compounds bound by one protein would bind the other. The method reproduces 84% of complexes in a benchmark, and we make many predictions that would not be possible using conventional modeling techniques. Within 19,578 novel predicted interactions are 7,793 involving 718 drugs, including filaminast, coumarin, alitretonin and erlotinib. The growth rate of confident predictions is twice that of experimental complexes, meaning that a complete structural drug-protein repertoire will be available at least ten years earlier than by X-ray and NMR techniques alone.