We demonstrate nonvolatile resistive switching in single crystalline ZnO nanowires with high ON/OFF ratios and low threshold voltages. Unlike the mechanism of continuous metal filament formation along grain boundaries in polycrystalline films, the resistive switching in single crystalline ZnO nanowires is speculated to be induced by the formation of a metal island chain on the nanowire surface. Resistive memories based on bottom-up semiconductor nanowires hold potential for next generation ultra-dense nonvolatile memories.