The ability to learn about regularities in the environment and to make predictions about future events is fundamental for adaptive behaviour. We have previously shown that people can implicitly encode statistical regularities and detect violations therein, as reflected in neuronal responses to unpredictable events that carry a unique prediction error signature. In the real world, however, learning about regularities will often occur in the context of competing cognitive demands. Here we asked whether learning of statistical regularities is modulated by concurrent cognitive load. We compared electroencephalographic metrics associated with responses to pure-tone sounds with frequencies sampled from narrow or wide Gaussian distributions. We showed that outliers evoked a larger response than those in the centre of the stimulus distribution (i.e., an effect of surprise) and that this difference was greater for physically identical outliers in the narrow than in the broad distribution. These results demonstrate an early neurophysiological marker of the brain’s ability to implicitly encode complex statistical structure in the environment. Moreover, we manipulated concurrent cognitive load by having participants perform a visual working memory task while listening to these streams of sounds. We again observed greater prediction error responses in the narrower distribution under both low and high cognitive load. Furthermore, there was no reliable reduction in prediction error magnitude under high-relative to low-cognitive load. Our findings suggest that statistical learning is not a capacity limited process, and that it proceeds automatically even when cognitive resources are taxed by concurrent demands.