Paralysis following spinal cord injury, brainstem stroke, amyotrophic lateral sclerosis and other disorders can disconnect the brain from the body, eliminating the ability to perform volitional movements. A neural interface system could restore mobility and independence for people with paralysis by translating neuronal activity directly into control signals for assistive devices. We have previously shown that people with long-standing tetraplegia can use a neural interface system to move and click a computer cursor and to control physical devices. Able-bodied monkeys have used a neural interface system to control a robotic arm, but it is unknown whether people with profound upper extremity paralysis or limb loss could use cortical neuronal ensemble signals to direct useful arm actions. Here we demonstrate the ability of two people with long-standing tetraplegia to use neural interface system-based control of a robotic arm to perform three-dimensional reach and grasp movements. Participants controlled the arm and hand over a broad space without explicit training, using signals decoded from a small, local population of motor cortex (MI) neurons recorded from a 96-channel microelectrode array. One of the study participants, implanted with the sensor 5 years earlier, also used a robotic arm to drink coffee from a bottle. Although robotic reach and grasp actions were not as fast or accurate as those of an able-bodied person, our results demonstrate the feasibility for people with tetraplegia, years after injury to the central nervous system, to recreate useful multidimensional control of complex devices directly from a small sample of neural signals.