EEG and eye-tracking provide complementary information when investigating language comprehension. Evidence that speech processing may be facilitated by speech prediction comes from the observation that a listener's eye gaze moves towards a referent before it is mentioned if the remainder of the spoken sentence is predictable. However, changes to the trajectory of anticipatory fixations could result from a change in prediction or an attention shift. Conversely, N400 amplitudes and concurrent spectral power provide information about the ease of word processing the moment the word is perceived. In a proof-of-principle investigation, we combined EEG and eye-tracking to study linguistic prediction in naturalistic, virtual environments. We observed increased processing, reflected in theta band power, either during verb processing - when the verb was predictive of the noun - or during noun processing - when the verb was not predictive of the noun. Alpha power was higher in response to the predictive verb and unpredictable nouns. We replicated typical effects of noun congruence but not predictability on the N400 in response to the noun. Thus, the rich visual context that accompanied speech in virtual reality influenced language processing compared to previous reports, where the visual context may have facilitated processing of unpredictable nouns. Finally, anticipatory fixations were predictive of spectral power during noun processing and the length of time fixating the target could be predicted by spectral power at verb onset, conditional on the object having been fixated. Overall, we show that combining EEG and eye-tracking provides a promising new method to answer novel research questions about the prediction of upcoming linguistic input, for example, regarding the role of extralinguistic cues in prediction during language comprehension.