Developing artificial tactile sensing capabilities that rival human touch is a long-term goal in robotics and prosthetics. Gradually more elaborate biomimetic tactile sensors are being developed and applied to grasping and manipulation tasks to help achieve this goal. Here we present the neuroTac, a novel neuromorphic optical tactile sensor. The neuroTac combines the biomimetic hardware design from the TacTip sensor which mimicks the layered papillae structure of human glabrous skin, with an event-based camera (DAVIS240, iniVation) and algorithms which transduce contact information in the form of spike trains. The performance of the sensor is evaluated on a texture classification task, with four spike coding methods being implemented and compared: Intensive, Spatial, Temporal and Spatiotemporal. We found timing-based coding methods performed with the highest accuracy over both artificial and natural textures. The spike-based output of the neuroTac could enable the development of biomimetic tactile perception algorithms in robotics as well as non-invasive and invasive haptic feedback methods in prosthetics.