The surface electrical properties of ZnO thin films grown along the nonpolar [1120] direction have been investigated by Kelvin probe microscopy on a nanometer scale. Two different charge domains, with a 75 meV work function difference, coexist within the ZnO surface, which is covered by rhombohedral pyramids whose sidewalls are shown to be {1011}-type planes. The presence and relative orientation of the two kinds of charge domains are explained in terms of the atomic arrangement at the {1011} polar surfaces.