Studies that use measures of cerebro-acoustic coherence have shown that theta oscillations (3–10 Hz) entrain to syllable-size modulations in the energy envelope of speech. This entrainment creates sensory windows in processing acoustic cues. Recent reports submit that delta oscillations (<3 Hz) can be entrained by nonsensory content units like phrases and serve to process meaning—though such views face fundamental problems. Other studies suggest that delta underlies a sensory chunking linked to the processing of sequential attributes of speech sounds. This chunking associated with the “focus of attention” is commonly manifested by the temporal grouping of items in sequence recall. Similar grouping in speech may entrain delta. We investigate this view by examining how low-frequency oscillations entrain to three types of stimuli (tones, nonsense syllables, and utterances) having similar timing, pitch, and energy contours. Entrainment was indexed by “intertrial phase coherence” in the EEGs of 18 listeners. The results show that theta oscillations at central sites entrain to syllable-size elements in speech and tones. However, delta oscillations at frontotemporal sites specifically entrain to temporal groups in both meaningful utterances and meaningless syllables, which indicates that delta may support but does not directly bear on a processing of content. The findings overall suggest that, although theta entrainment relates to a processing of acoustic attributes, delta entrainment links to a sensory chunking that relates to a processing of properties of articulated sounds. The results also show that measures of intertrial phase coherence can be better suited than cerebro-acoustic coherence in revealing delta entrainment.