Adverse Drug Reactions (ADRs) are unintentional reactions caused by a drug or combination of drugs taken by a patient. The current ADR reporting systems inevitably have delays in reporting such events. The broad scope of social media conversations on sites such as Twitter means that inevitably health-related topics will be covered. This means that these sites could then be used to detect potentially novel ADRs with less latency for subsequent further investigation. In this work, we investigate ADR surveillance using a large corpus of Twitter data, containing around 50 billion tweets spanning 3 years (2012-2014), and evaluate against over 3000 drugs reported in the FAERS database. This is both a larger corpus and broader selection of drugs than previous work in the domain. We compare the ADRs identified using our method to the FDA Adverse Event Reporting System (FAERS) database of ADRs reported using more traditional techniques, and find that Twitter is a useful resource for ADR detection up to 72% micro-averaged precision. Micro-averaged recall of 6% is achievable using only 10% of Twitter, indicating that with a higher-volume or targeted feed it would be possible to detect a large percentage of ADRs.