In many complex social systems, the timing and frequency of interactions between individuals are observable but friendship ties are hidden. Recovering these hidden ties, particularly for casual users who are relatively less active, would enable a wide variety of friendship-aware applications in domains where labeled data are often unavailable, including online advertising and national security. Here, we investigate the accuracy of multiple statistical features, based either purely on temporal interaction patterns or on the cooperative nature of the interactions, for automatically extracting latent social ties. Using self-reported friendship and non-friendship labels derived from an anonymous online survey, we learn highly accurate predictors for recovering hidden friendships within a massive online data set encompassing 18 billion interactions among 17 million individuals of the popular online game Halo: Reach. We find that the accuracy of many features improves as more data accumulates, and cooperative features are generally reliable. However, periodicities in interaction time series are sufficient to correctly classify 95% of ties, even for casual users. These results clarify the nature of friendship in online social environments and suggest new opportunities and new privacy concerns for friendship-aware applications that do not require the disclosure of private friendship information.