We introduce the first use of deep neural network-based generative modeling for high energy physics (HEP). Our novel Generative Adversarial Network (GAN) architecture is able cope with the key challenges in HEP images, including sparsity and a large dynamic range. For example, our Location-Aware Generative Adversarial Network learns to produce realistic radiation patterns inside high energy jets - collimated sprays of particles resulting from quarks and gluons produced at high energy. The pixel intensities of the GAN-generated images faithfully span many orders of magnitude and reproduce the distributions of important low-dimensional physical properties (e.g. jet mass, n-subjettiness, etc.). We provide many visualizations of what the GAN has learned, to build additional confidence in the algorithm. Our results demonstrate that high-fidelity, fast simulation through GANs is a promising application of deep neural networks for solving one of the most important challenges facing HEP today.