Functional electrical stimulation (FES) is a promising technique for restoring reaching ability to individuals with tetraplegia. To this point, the complexities of goal-directed reaching motions and the shoulder-arm complex have prevented the realization of this potential in full-arm 3D reaching tasks. We trained a Gaussian process regression model to form the basis of a feedforward-feedback control structure capable of achieving reaching motions with a paralyzed upper limb. Over a series of 95 reaches of at least 10 cm in length, the controller achieved an average accuracy (measured by the Euclidean distance of the wrist to the final target position) of 3.8 cm and an average error along the path of 3.5 cm. This controller is the first demonstration of an accurate, complete-arm, FES-driven 3D reaching controller to be implemented with an individual with tetraplegia.