ZnO channel waveguides were fabricated for the first time, for the purpose of being used in nonlinear optical applications. Wide-bandgap ZnO was chosen for the core material to avoid two-photon absorption at wavelengths above 800nm which are used for biomedical applications. We calculated the single-mode conditions and group-velocity dispersion of the propagating modes for the waveguides. We also fabricated channel waveguides using single-crystal ZnO thin film grown on sapphire substrate. Measured propagation losses with a cut-back method were approximately 3 to 6 dB/mm for single-mode waveguides.