This work addresses the challenging task of LiDAR-based 3D object detection in foggy weather. Collecting and annotating data in such a scenario is very time, labor and cost intensive. In this paper, we tackle this problem by simulating physically accurate fog into clear-weather scenes, so that the abundant existing real datasets captured in clear weather can be repurposed for our task. Our contributions are twofold: 1) We develop a physically valid fog simulation method that is applicable to any LiDAR dataset. This unleashes the acquisition of large-scale foggy training data at no extra cost. These partially synthetic data can be used to improve the robustness of several perception methods, such as 3D object detection and tracking or simultaneous localization and mapping, on real foggy data. 2) Through extensive experiments with several state-of-the-art detection approaches, we show that our fog simulation can be leveraged to significantly improve the performance for 3D object detection in the presence of fog. Thus, we are the first to provide strong 3D object detection baselines on the Seeing Through Fog dataset. Our code is available at www.trace.ethz.ch/lidar_fog_simulation.