We introduce a stereo correspondence system implemented fully on event-based digital hardware, using a fully graph-based non von-Neumann computation model, where no frames, arrays, or any other such data-structures are used. This is the first time that an end-to-end stereo pipeline from image acquisition and rectification, multi-scale spatiotemporal stereo correspondence, winner-take-all, to disparity regularization is implemented fully on event-based hardware. Using a cluster of TrueNorth neurosynaptic processors, we demonstrate their ability to process bilateral event-based inputs streamed live by Dynamic Vision Sensors (DVS), at up to 2,000 disparity maps per second, producing high fidelity disparities which are in turn used to reconstruct, at low power, the depth of events produced from rapidly changing scenes. Experiments on real-world sequences demonstrate the ability of the system to take full advantage of the asynchronous and sparse nature of DVS sensors for low power depth reconstruction, in environments where conventional frame-based cameras connected to synchronous processors would be inefficient for rapidly moving objects. System evaluation on event-based sequences demonstrates a ~ 200 Ã - improvement in terms of power per pixel per disparity map compared to the closest state-of-the-art, and maximum latencies of up to 11ms from spike injection to disparity map ejection.