Spontaneous speech is produced in chunks called Intonation Units (IUs). IUs are defined by a set of prosodic cues and occur in all human languages. Linguistic theory suggests that IUs pace the flow of information and serve as a window onto the dynamic focus of attention in speech processing. IUs provide a promising and hitherto unexplored theoretical framework for studying the neural mechanisms of communication, thanks to their universality and their consistent temporal structure across different grammatical and socio-cultural conditions. In this article, we identify a neural response unique to the boundary defined by the IU. We measured the EEG of participants who listened to different speakers recounting an emotional life event. We analyzed the speech stimuli linguistically, and modeled the EEG response at word offset using a GLM approach. We find that the EEG response to IU-final words differs from the response to IU-nonfinal words when acoustic boundary strength is held constant. To the best of our knowledge, this is the first time this is demonstrated in spontaneous speech under naturalistic listening conditions, and under a theoretical framework that connects the prosodic chunking of speech, on the one hand, with the flow of information during communication, on the other. Finally, we relate our findings to the body of research on rhythmic brain mechanism in speech processing by comparing the topographical distributions of neural speech tracking in model-predicted and empirical EEG. This qualitative comparison suggests that IU-related neural activity contributes to the previously characterized delta-band neural speech tracking.