We present CoverNet, a new method for multimodal, probabilistic trajectory prediction for urban driving. Previous work has employed a variety of methods, including multimodal regression, occupancy maps, and 1-step stochastic policies. We instead frame the trajectory prediction problem as classification over a diverse set of trajectories. The size of this set remains manageable due to the limited number of distinct actions that can be taken over a reasonable prediction horizon. We structure the trajectory set to a) ensure a desired level of coverage of the state space, and b) eliminate physically impossible trajectories. By dynamically generating trajectory sets based on the agent’s current state, we can further improve our method’s efficiency. We demonstrate our approach on public, real-world self-driving datasets, and show that it outperforms state-of-the-art methods.