Neurophysiological studies in humans and nonhuman primates have revealed movement representations in both the contralateral and ipsilateral hemispheres. Inspired by clinical observations, we ask if this bilateral representation differs for the left and right hemispheres. Electrocorticography was recorded in human participants during an instructed-delay reaching task, with movements produced with either the contralateral or ipsilateral arm. Using a cross-validated kinematic encoding model, we found stronger bilateral encoding in the left hemisphere, an effect that was present during preparation and was amplified during execution. Consistent with this asymmetry, we also observed better across-arm generalization in the left hemisphere, indicating similar neural representations for right and left arm movements. Notably, these left hemisphere electrodes were centered over premotor and parietal regions. The more extensive bilateral encoding in the left hemisphere adds a new perspective to the pervasive neuropsychological finding that the left hemisphere plays a dominant role in praxis.