Charged (e.g., colloidal) particles in aqueous solutions will sometimes behave as though their effective charge has reversed, rather than reduced, by the attracted counterions. This is counterintuitive because it increases the electrostatic energy, but it has been proposed that lateral ordering of the ions could lower the free energy and favor overcharging (charge inversion). Using X-ray diffraction, we have observed sharp diffraction peaks from incommensurate Er(3+) counterion monolayers near charged surfaces formed by floating molecular monolayers. When the counterion lattice does not match the molecular surface lattice, this means that there is no specific attachment of ions, and thus the ionic lattice is formed due to interactions between charges in the counterlayer. Therefore, the existence of incommensurate ion lattices indicates that counterion ordering is a realistic mechanism. However, in this system our data rule out a well-known proposed "physical" mechanism-the Wigner liquid phase driven by Coulomb interactions.