To use deep reinforcement learning in the wild, we might hope for an agent that can avoid catastrophic mistakes. Unfortunately, even in simple environments, the popular deep Q-network (DQN) algorithm is doomed by a Sisyphean curse. Owing to the use of function approximation, these agents eventually forget experiences as they become exceedingly unlikely under a new policy. Consequently, for as long as they continue to train, DQNs may periodically relive catastrophic mistakes. Many real-world environments where people might be injured exhibit a special structure. We know a priori that catastrophes are not only bad, but that agents need not ever get near to a catastrophe state. In this paper, we exploit this structure to learn a reward-shaping that accelerates learning and guards oscillating policies against repeated catastrophes. First, we demonstrate unacceptable performance of DQNs on two toy problems. We then introduce intrinsic fear, a new method that mitigates these problems by avoiding dangerous states. Our approach incorporates a second model trained via supervised learning to predict the probability of catastrophe within a short number of steps. This score then acts to penalize the Q-learning objective, shaping the reward function away from catastrophic states.