In this paper we show that High-Definition (HD) maps provide strong priors that can boost the performance and robustness of modern 3D object detectors. Towards this goal, we design a single stage detector that extracts geometric and semantic features from the HD maps. As maps might not be available everywhere, we also propose a map prediction module that estimates the map on the fly from raw LiDAR data. We conduct extensive experiments on KITTI  as well as a large-scale 3D detection benchmark containing 1 million frames, and show that the proposed map-aware detector consistently outperforms the state-of-the-art in both mapped and un-mapped scenarios. Importantly the whole framework runs at 20 frames per second.