This paper focuses on a three-parameter deformation of N=4 Yang-Mills that breaks all the supersymmetry in the theory. We show that the resulting non-supersymmetric gauge theory is conformally invariant, in the planar approximation, by proving that its Green functions are ultra-violet finite to all orders in light-cone perturbation theory. We explain the subtleties associated with proving ultraviolet finiteness, even in the planar limit, for deformations of N=4 Yang-Mills.