Social networks are often grounded in spatial locality where individuals form relationships with those they meet nearby. However, the location of individuals in online social networking platforms is often unknown. Prior approaches have tried to infer individuals' locations from the content they produce online or their online relations, but often are limited by the available location-related data. We propose a new method for social networks that accurately infers locations for nearly all of individuals by spatially propagating location assignments through the social network, using only a small number of initial locations. In five experiments, we demonstrate the effectiveness in multiple social networking platforms, using both precise and noisy data to start the inference, and present heuristics for improving performance. In one experiment, we demonstrate the ability to infer the locations of a group of users who generate over 74% of the daily Twitter message volume with an estimated median location error of 10km. Our results open the possibility of gathering large quantities of location-annotated data from social media platforms.