Over the last few years, we have witnessed tremendous progress on many subtasks of autonomous driving, including perception, motion forecasting, and motion planning. However, these systems often assume that the car is accurately localized against a high-definition map. In this paper we question this assumption, and investigate the issues that arise in state-of-the-art autonomy stacks under localization error. Based on our observations, we design a system that jointly performs perception, prediction, and localization. Our architecture is able to reuse computation between both tasks, and is thus able to correct localization errors efficiently. We show experiments on a large-scale autonomy dataset, demonstrating the efficiency and accuracy of our proposed approach.