Optical dipole traps and atom chips are two very powerful tools for the quantum manipulation of neutral atoms. We demonstrate that both methods can be combined by creating an optical lattice potential on an atom chip. A red-detuned laser beam is retro-reflected using the atom chip surface as a high-quality mirror, generating a vertical array of purely optical oblate traps. We load thermal atoms from the chip into the lattice and observe cooling into the two-dimensional regime where the thermal energy is smaller than a quantum of transverse excitation. Using a chip-generated Bose-Einstein condensate, we demonstrate coherent Bloch oscillations in the lattice.