Loihi is a 60-mm2 chip fabricated in Intels 14-nm process that advances the state-of-the-art modeling of spiking neural networks in silicon. It integrates a wide range of novel features for the field, such as hierarchical connectivity, dendritic compartments, synaptic delays, and, most importantly, programmable synaptic learning rules. Running a spiking convolutional form of the Locally Competitive Algorithm, Loihi can solve LASSO optimization problems with over three orders of magnitude superior energy-delay-product compared to conventional solvers running on a CPU iso-process/voltage/area. This provides an unambiguous example of spike-based computation, outperforming all known conventional solutions.