A lattice beam configuration that results in an isotropic 3D trap near the surface of an atom chip is described. The lattice is formed near the surface of a reflectively coated atom chip, where three incident beams and three reflected beams intersect. The coherent interference of these six beams forms a phase-stable optical lattice that extends to the surface of the atom chip. The lattice is experimentally realized, and the trap frequency is measured. Degenerate Raman sideband cooling is performed in the optical lattice, cooling 80 million atoms to .