End-to-end approaches to autonomous driving commonly rely on expert demonstrations. Although humans are good drivers, they are not good coaches for end-to-end algorithms that demand dense on-policy supervision. On the contrary, automated experts that leverage privileged information can efficiently generate large scale on-policy and off-policy demonstrations. However, existing automated experts for urban driving make heavy use of hand-crafted rules and perform suboptimally even on driving simulators, where ground-truth information is available. To address these issues, we train a reinforcement learning expert that maps bird's-eye view images to continuous low-level actions. While setting a new performance upper-bound on CARLA, our expert is also a better coach that provides informative supervision signals for imitation learning agents to learn from. Supervised by our reinforcement learning coach, a baseline end-to-end agent with monocular camera-input achieves expert-level performance. Our end-to-end agent achieves a 78% success rate while generalizing to a new town and new weather on the NoCrash-dense benchmark and state-of-the-art performance on the challenging public routes of the CARLA LeaderBoard.