Localization is a key task for autonomous vehicles. It is often solved with GNSS but due to multipath the performance is often not sufficient. Feature localization systems using LiDAR can deliver an accurate localization but the creation of the necessary feature maps is an effortful task. With digitization of urban planning processes a lot of street level data is being generated and increasingly becomes openly available. We propose a novel feature localization system which utilizes geometric fingerprinting to robustly associate features to a feature map generated from this open data from the city of Berlin. With this association, we perform a precise localization of a vehicle in areas spanning over several square kilometers using an optional IMU, the vehicle's CAN-odometry and an initial pose estimate. We evaluated our system with our autonomous car in real world scenarios and achieved a centimeter precision localization accuracy outperforming a high-cost GNSS. The source code will be published at https://github.com/dcmlr/fingerprint-localization.