Social interactions and interpersonal communication has undergone significant changes in recent years. Increasing awareness of privacy issues and events such as the Snowden disclosures have led to the rapid growth of a new generation of anonymous social networks and messaging applications. By removing traditional concepts of strong identities and social links, these services encourage communication between strangers, and allow users to express themselves without fear of bullying or retaliation. Despite millions of users and billions of monthly page views, there is little empirical analysis of how services like Whisper have changed the shape and content of social interactions. In this paper, we present results of the first large-scale empirical study of an anonymous social network, using a complete 3-month trace of the Whisper network covering 24 million whispers written by more than 1 million unique users. We seek to understand how anonymity and the lack of social links affect user behavior. We analyze Whisper from a number of perspectives, including the structure of user interactions in the absence of persistent social links, user engagement and network stickiness over time, and content moderation in a network with minimal user accountability. Finally, we identify and test an attack that exposes Whisper users to detailed location tracking. We have notified Whisper and they have taken steps to address the problem.