We propose a novel method of regularization for recurrent neural networks called suprisal-driven zoneout. In this method, states zoneout (maintain their previous value rather than updating), when the suprisal (discrepancy between the last state's prediction and target) is small. Thus regularization is adaptive and input-driven on a per-neuron basis. We demonstrate the effectiveness of this idea by achieving state-of-the-art bits per character of 1.31 on the Hutter Prize Wikipedia dataset, significantly reducing the gap to the best known highly-engineered compression methods.