Event cameras are bio-inspired vision sensors that output pixel-level brightness changes instead of standard intensity frames. They offer significant advantages over standard cameras, namely a very high dynamic range, no motion blur, and a latency in the order of microseconds. However, because the output is composed of a sequence of asynchronous events rather than actual intensity images, traditional vision algorithms cannot be applied, so that a paradigm shift is needed. We introduce the problem of event-based multi-view stereo (EMVS) for event cameras and propose a solution to it. Unlike traditional MVS methods, which address the problem of estimating dense 3D structure from a set of known viewpoints, EMVS estimates semi-dense 3D structure from an event camera with known trajectory. Our EMVS solution elegantly exploits two inherent properties of an event camera: (1) its ability to respond to scene edges—which naturally provide semi-dense geometric information without any pre-processing operation—and (2) the fact that it provides continuous measurements as the sensor moves. Despite its simplicity (it can be implemented in a few lines of code), our algorithm is able to produce accurate, semi-dense depth maps, without requiring any explicit data association or intensity estimation. We successfully validate our method on both synthetic and real data. Our method is computationally very efficient and runs in real-time on a CPU.