In this work, the structure of the tetraphenylporphyrin (H2TPP) monolayer grown on the oxygen passivated Cu(110)-(2 × 1)O surface has been investigated with LT-STM and elucidated by DFT-calculations. The monolayer is commensurate with all molecules occupying the same adsorption site, but there are two molecules per unit cell. The STM images suggest alternating chirality for the molecules within one unit cell which is supported by DFT total energy calculations for monolayers on the Cu-O substrate. STM simulations for alternating and single chirality monolayers have subtle differences which indicate that the experimentally observed surface is one containing molecules with alternating chirality, that is racemicity within the unit cell.