The electronic structure around the Fermi energy of a thin film of iron monoxide on Pt͑111͒ is studied using low temperature scanning tunneling spectroscopy. The surface exhibits a coincidence structure ͑Moiré pattern͒ due to a lattice mismatch between the oxide thin film and the metal substrate. While the local density of states around the Fermi energy is featureless at most positions in the unit cell, a pronounced depression is observed at one particular site. The origin of this local zero-bias anomaly is discussed in relation to results from first-principle calculations. As a preliminary conclusion, it is suggested that the anomaly is a Kondo resonance due to a frustrated antiferromagnetic layer.