Autonomous car racing is a major challenge in robotics. It raises fundamental problems for classical approaches such as planning minimum-time trajectories under uncertain dynamics and controlling the car at the limits of its handling. Besides, the requirement of minimizing the lap time, which is a sparse objective, and the difficulty of collecting training data from human experts have also hindered researchers from directly applying learning-based approaches to solve the problem. In the present work, we propose a learning-based system for autonomous car racing by leveraging a high-fidelity physical car simulation, a course-progress proxy reward, and deep reinforcement learning. We deploy our system in Gran Turismo Sport, a world-leading car simulator known for its realistic physics simulation of different race cars and tracks, which is even used to recruit human race car drivers. Our trained policy achieves autonomous racing performance that goes beyond what had been achieved so far by the built-in AI, and, at the same time, outperforms the fastest driver in a dataset of over 50,000 human players.