In this paper, we propose a neural motion planner (NMP) for learning to drive autonomously in complex urban scenarios that include traffic-light handling, yielding, and interactions with multiple road-users. Towards this goal, we design a holistic model that takes as input raw LIDAR data and a HD map and produces interpretable intermediate representations in the form of 3D detections and their future trajectories, as well as a cost volume defining the goodness of each position that the self-driving car can take within the planning horizon. We then sample a set of diverse physically possible trajectories and choose the one with the minimum learned cost. Importantly, our cost volume is able to naturally capture multi-modality. We demonstrate the effectiveness of our approach in real-world driving data captured in several cities in North America. Our experiments show that the learned cost volume can generate safer planning than all the baselines.