We describe and validate a system for monitoring social contagions on Twitter: social movements, rumors, and emotional outbursts that spread from person to person in a viral manner. We use Twitter streams to monitor the spread of these phenomena through human social and information networks. This system, the contagion monitor, parses Twitter posts to identify emerging phenomena, as captured in hashtags, URLs, words and phrases, or account-handles, and then determines the extent to which a particular phenomenon spreads via the social network (in contrast to its spread via news broadcasts or independent adoption) and locates the contagion within Twitter communities. The monitor approximates the adoption threshold of a social contagion by measuring the fraction of Twitter users who were "infected" by the contagion (e.g., joined a particular social movement) after more than one of their friends had done so. Finally, the monitor makes a judgment about whether the phenomenon has reached critical mass, which is defined as the point where a social contagion begins spreading rapidly and breaches the social boundaries of its early adopter group. We test our prototype monitor on two data sources - an ongoing stream of tweets grouped by user-added hashtags and a collection of posts by a monitored set of Nigerian Twitter users - before productionalizing. We use the Amazon Mechanical Turk platform to evaluate the performance on both data sources. In both cases, we find that our approach successfully distinguishes between high-threshold and low-threshold social contagions.