A three-dimensional (3D) lattice of nanoscale coated spheres is shown to have an isotropic negative index of refraction at optical frequencies. The nanospheres have a core of copper chloride (CuCl) and are coated by a layer of silver. The extended Maxwell Garnett model, relating the Mie resonances of the constituent spheres to the bulk response of the composite, is used for the design. The results for the effective parameters are then verified by supplemental calculations with a homogenization method taking into account interaction effects due to higher order multipoles in close-packed arrays. The possibility of realizing metamaterials exhibiting negative index in the visible with large figure of merit is demonstrated.