Speech comprehension requires rapid online processing of a continuous acoustic signal to extract structure and meaning. Previous studies on sentence comprehension have found neural correlates of the predictability of a word given its context, as well as a of the precision of such a prediction. However, they have focussed on single sentences and on particular words in those sentences. Moreover, they compared neural responses to words with low and high predictability, as well as with low and high precision. However, in speech comprehension a listener hears many successive words whose predictability and precision vary over a large range. Here we show that cortical activity in different frequency bands tracks word surprisal in continuous natural speech, and that this tracking is modulated by precision. We obtain these results through quantifying surprisal and precision from naturalistic speech using a deep neural network, and through relating these speech features to electroencephalographic (EEG) responses of human volunteers acquired during auditory story comprehension. We find significant cortical tracking of surprisal at low frequencies including the delta band as well as in the higher-frequency beta and gamma bands, and observe that the tracking is modulated by the precision. Our results pave the way to further investigate the neurobiology of natural speech comprehension.