Prediction in language has traditionally been studied using simple designs in which neural responses to expected and unexpected words are compared in a categorical fashion. However, these designs have been contested as being `prediction encouraging', potentially exaggerating the importance of prediction in language understanding. A few recent studies have begun to address these worries by using model-based approaches to probe the effects of linguistic predictability in naturalistic stimuli (e.g. continuous narrative). However, these studies so far only looked at very local forms of prediction, using models that take no more than the prior two words into account when computing a word's predictability. Here, we extend this approach using a state-of-the-art neural language model that can take roughly 500 times longer linguistic contexts into account. Predictability estimates from the neural network offer a much better fit to EEG data from subjects listening to naturalistic narrative than simpler models, and reveal strong surprise responses akin to the P200 and N400. These results show that predictability effects in language are not a side-effect of simple designs, and demonstrate the practical use of recent advances in AI for the cognitive neuroscience of language.