Rumours can spread quickly through social media, and malicious ones can bring about significant economical and social impact. Motivated by this, our paper focuses on the task of rumour detection; particularly, we are interested in understanding how early we can detect them. Although there are numerous studies on rumour detection, few are concerned with the timing of the detection. A successfully-detected malicious rumour can still cause significant damage if it isn't detected in a timely manner, and so timing is crucial. To address this, we present a novel methodology for early rumour detection. Our model treats social media posts (e.g. tweets) as a data stream and integrates reinforcement learning to learn the number minimum number of posts required before we classify an event as a rumour. Experiments on Twitter and Weibo demonstrate that our model identifies rumours earlier than state-of-the-art systems while maintaining a comparable accuracy.