Social relationships are a natural basis on which humans make trust decisions. Online Social Networks (OSNs) are increasingly often used to let users base trust decisions on the existence and the strength of social relationships. While most OSNs allow users to discover the length of the social path to other users, they do so in a centralized way, thus requiring them to rely on the service provider and reveal their interest in each other. This paper presents Social PaL, a system supporting the privacy-preserving discovery of arbitrary-length social paths between any two social network users. We overcome the bootstrapping problem encountered in all related prior work, demonstrating that Social PaL allows its users to find all paths of length two and to discover a significant fraction of longer paths, even when only a small fraction of OSN users is in the Social PaL system - e.g., discovering 70% of all paths with only 40% of the users. We implement Social PaL using a scalable server-side architecture and a modular Android client library, allowing developers to seamlessly integrate it into their apps.