This paper explores the potential of event cameras to enable continuous time reinforcement learning. We formalise this problem where a continuous stream of unsynchronised observations is used to produce a corresponding stream of output actions for the environment. This lack of synchronisation enables greatly enhanced reactivity. We present a method to train on event streams derived from standard RL environments, thereby solving the proposed continuous time RL problem. The CERiL algorithm uses specialised network layers which operate directly on an event stream, rather than aggregating events into quantised image frames. We show the advantages of event streams over less-frequent RGB images. The proposed system outperforms networks typically used in RL, even succeeding at tasks which cannot be solved traditionally. We also demonstrate the value of our CERiL approach over a standard SNN baseline using event streams.