Oscillation-based models of speech perception postulate a cortical computational principle by which decoding is performed within a window structure derived by a segmentation process. Segmentation of syllable-size chunks is realized by a theta oscillator. We provide evidence for an analogous role of a delta oscillator in the segmentation of phrase-sized chunks. We recorded Magnetoencephalography (MEG) in humans, while participants performed a target identification task. Random-digit strings, with phrase-long chunks of two digits, were presented at chunk rates of 1.8 Hz or 2.6 Hz, inside or outside the delta frequency band (defined here to be 0.5 -2 Hz). Strong periodicities were elicited by chunk rates inside of delta in superior, middle temporal areas and speech-motor integration areas. Periodicities were diminished or absent for chunk rates outside delta, in line with behavioral performance. Our findings show that prosodic chunking of phrase-sized acoustic segments is correlated with acoustic-driven delta oscillations, expressing anatomically specific patterns of neuronal periodicities.