Natural speech builds on contextual relations that can prompt predictions of upcoming utterances. To study the neural underpinnings of such predictive processing we asked 10 healthy adults to listen to a 1-h-long audiobook while their magnetoencephalographic (MEG) brain activity was recorded. We correlated the MEG signals with acoustic speech envelope, as well as with estimates of Bayesian word probability with and without the contextual word sequence (N-gram and Unigram, respectively), with a focus on time-lags. The MEG signals of auditory and sensorimotor cortices were strongly coupled to the speech envelope at the rates of syllables (4–8 Hz) and of prosody and intonation (0.5–2 Hz). The probability structure of word sequences, independently of the acoustical features, affected the ≤ 2-Hz signals extensively in auditory and rolandic regions, in precuneus, occipital cortices, and lateral and medial frontal regions. Fine-grained temporal progression patterns occurred across brain regions 100–1000 ms after word onsets. Although the acoustic effects were observed in both hemispheres, the contextual influences were statistically significantly lateralized to the left hemisphere. These results serve as a brain signature of the predictability of word sequences in listened continuous speech, confirming and extending previous results to demonstrate that deeply-learned knowledge and recent contextual information are employed dynamically and in a left-hemisphere-dominant manner in predicting the forthcoming words in natural speech.