This paper introduces BinarEye: a digital processor for always-on Binary Convolutional Neural Networks. The chip maximizes data reuse through a Neuron Array exploiting local weight Flip-Flops. It stores full network models and feature maps and hence requires no off-chip bandwidth, which leads to a 230 1b-TOPS/W peak efficiency. Its 3 levels of flexibility - (a) weight reconfiguration, (b) a programmable network depth and (c) a programmable network width - allow trading energy for accuracy depending on the task's requirements. BinarEye's full system input-to-label energy consumption ranges from 14.4uJ/f for 86% CIFAR-10 and 98% owner recognition down to 0.92uJ/f for 94% face detection at up to 1700 frames per second. This is 3-12-70x more efficient than the state-of-the-art at on-par accuracy.