In this paper, we propose a neural motion planner 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 an 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 and uncertainty. We demonstrate the effectiveness of our approach in real-world driving data captured in several cities in North America.