Modern graphics processing units (GPUs) are flexibly programmable and have peak computational throughput significantly faster than conventional CPUs. Herein, we describe the design and implementation of PAPER, an open-source implementation of Gaussian molecular shape overlay for NVIDIA GPUs. We demonstrate one to two order-of-magnitude speedups on high-end commodity GPU hardware relative to a reference CPU implementation of the shape overlay algorithm and speedups of over one order of magnitude relative to the commercial OpenEye ROCS package. In addition, we describe errors incurred by approximations used in common implementations of the algorithm.