Viewing a speaker's lip movements can improve the brain's ability to 'track' the amplitude envelope of the auditory speech signal and facilitate intelligibility. Whether such neurobehavioral benefits can also arise from tactually sensing the speech envelope on the skin is unclear. We hypothesized that tactile speech envelopes can improve neural tracking of auditory speech and thereby facilitate intelligibility. To test this, we applied continuous auditory speech and vibrotactile speech-envelope-shaped stimulation at various asynchronies to the ears and index fingers of normally-hearing human listeners while simultaneously assessing speech-recognition performance and cortical speech-envelope tracking with electroencephalography. Results indicate that tactile speech-shaped envelopes improve the cortical tracking, but not intelligibility, of degraded auditory speech. The cortical speech-tracking benefit occurs for tactile input leading the auditory input by 100 m s or less, emerges in the EEG during an early time window (∼0-150 m s), and in particular involves cortical activity in the delta (1-4 Hz) range. These characteristics hint at a predictive mechanism for multisensory integration of complex slow time-varying inputs that might play a role in tactile speech communication.