The study of the production of co-speech gestures (CSGs), i.e., meaningful hand movements that often accompany speech during everyday discourse, provides an important opportunity to investigate the integration of language, action, and memory because of the semantic overlap between gesture movements and speech content. Behavioral studies of CSGs and speech suggest that they have a common base in memory and predict that overt production of both speech and CSGs would be preceded by neural activity related to memory processes. However, to date the neural correlates and timing of CSG production are still largely unknown. In the current study, we addressed these questions with magnetoencephalography and a semantic association paradigm in which participants overtly produced speech or gesture responses that were either meaningfully related to a stimulus or not. Using spectral and beamforming analyses to investigate the neural activity preceding the responses, we found a desynchronization in the beta band (15-25 Hz), which originated 900 ms prior to the onset of speech and was localized to motor and somatosensory regions in the cortex and cerebellum, as well as right inferior frontal gyrus. Beta desynchronization is often seen as an indicator of motor processing and thus reflects motor activity related to the hand movements that gestures add to speech. Furthermore, our results show oscillations in the high gamma band (50-90 Hz), which originated 400 ms prior to speech onset and were localized to the left medial temporal lobe. High gamma oscillations have previously been found to be involved in memory processes and we thus interpret them to be related to contextual association of semantic information in memory. The results of our study show that high gamma oscillations in medial temporal cortex play an important role in the binding of information in human memory during speech and CSG production.