Vision-based urban driving is hard. The autonomous system needs to learn to perceive the world and act in it. We show that this challenging learning problem can be simplified by decomposing it into two stages. We first train an agent that has access to privileged information. This privileged agent cheats by observing the ground-truth layout of the environment and the positions of all traffic participants. In the second stage, the privileged agent acts as a teacher that trains a purely vision-based sensorimotor agent. The resulting sensorimotor agent does not have access to any privileged information and does not cheat. This two-stage training procedure is counter-intuitive at first, but has a number of important advantages that we analyze and empirically demonstrate. We use the presented approach to train a vision-based autonomous driving system that substantially outperforms the state of the art on the CARLA benchmark and the recent NoCrash benchmark. Our approach achieves, for the first time, 100% success rate on all tasks in the original CARLA benchmark, sets a new record on the NoCrash benchmark, and reduces the frequency of infractions by an order of magnitude compared to the prior state of the art.