Recent advances in the field of brain-machine interfaces (BMIs) have demonstrated enormous potential to shape the future of rehabilitation and prosthetic devices. Here, a lower-limb exoskeleton controlled by the intracortical activity of an awake behaving rhesus macaque is presented as a proof-of-concept for a locomotor BMI. A detailed description of the mechanical device, including its innovative features and first experimental results, is provided. During operation, BMI-decoded position and velocity are directly mapped onto the bipedal exoskeleton's motions, which then move the monkey's legs as the monkey remains physically passive. To meet the unique requirements of such an application, the exoskeleton's features include: high output torque with backdrivable actuation, size adjustability, and safe user-robot interface. In addition, a novel rope transmission is introduced and implemented. To test the performance of the exoskeleton, a mechanical assessment was conducted, which yielded quantifiable results for transparency, efficiency, stiffness, and tracking performance. Usage under both brain control and automated actuation demonstrates the device's capability to fulfill the demanding needs of this application. These results lay the groundwork for further advancement in BMI-controlled devices for primates including humans.