The physiological basis of human cerebral asymmetry for language remains mysterious. We have used simultaneous physiological and anatomical measurements to investigate the issue. Concentrating on neural oscillatory activity in speech-specific frequency bands and exploring interactions between gestural (motor) and auditory-evoked activity, we find, in the absence of language-related processing, that left auditory, somatosensory, articulatory motor, and inferior parietal cortices show specific, lateralized, speech-related physiological properties. With the addition of ecologically valid audiovisual stimulation, activity in auditory cortex synchronizes with left-dominant input from the motor cortex at frequencies corresponding to syllabic, but not phonemic, speech rhythms. Our results support theories of language lateralization that posit a major role for intrinsic, hardwired perceptuomotor processing in syllabic parsing and are compatible both with the evolutionary view that speech arose from a combination of syllable-sized vocalizations and meaningful hand gestures and with developmental observations suggesting phonemic analysis is a developmentally acquired process.