We investigate the extent to which word surprisal can be used to predict a neural measure of human language processing difficulty—the N400. To do this, we use recurrent neural networks to calculate the surprisal of stimuli from previously published neurolinguistic studies of the N400. We find that surprisal can predict N400 amplitude in a wide range of cases, and the cases where it cannot do so provide valuable insight into the neurocognitive processes underlying the response.