Today, advanced sensing technologies are one of the key drivers in many daily life application such as, driver assistance systems, autonomous robots in automation applications or autonomous vehicles. In particular the 3D perception of the environment in which these applications operate is crucial for a reliable function. For this, stereo vision can be used where the environment is observed with two digital cameras from two different points of view. Each point in the scene, visible to both cameras, is mapped onto both image planes, and thus, its projections correspond to each other and its 3D position can be reconstructed -- the spatial displacement of these projections is inversely proportional to the distance of the scene point. The main issue in stereo matching is solving the correspondence problem for a given stereo image pair. In fact, this is especially for high frame rates and spatial resolutions, a very time consuming and computationally expensive task. Furthermore, in most applications the observed scene does not change all the time, thus a lot of redundant data must be processed every time a new image pair is captured. Consequently, in this work a new kind of bio-inspired event-driven vision sensor is used delivering data only on illumination changes, completely asynchronously in time, called silicon retina. Such a sensor provides no frames, but a time-continuous stream of intensity differences and thus inherently reduces the visual information to a minimum. But in order to handle these sparse input data, a different algorithmic approach is required for event-based sensors. To this end, an event-based stereo matching approach based on time-correlation is introduced that allows a reliable matching of the sparse input event data. To address the high temporal resolution of the silicon retina and to do the correspondence search in real-time, the algorithm is implemented in hardware on a field programmable gate array (FPGA). Additionally, an automated stereo calibration method for silicon retinea is presented, enabling the calculation of the intrinsic and extrinsic parameters required for the rectification of the stereo event streams. Finally, an evaluation platform is introduced that enables ground truth based verification of the matching results, and a convincing comparison to other event-driven stereo matching algorithms. Real-world test cases have shown promising results in terms of accuracy measured by the average distance error. In particular, the area-based matching approach, that considers the spatial ordering of the events leads to confident and rather dense matching results in comparison to other matching algorithms.