The H-terminated n-Si(111) surface is found to be etched locally under the STM tip in the dilute HF solution by applying a given positive potential to the tip while keeping the silicon electrode potential near its flat-band potential, at which the oxidative etching of silicon is not expected to occur in the absence of light. The induced etching rate is shown to depend on the tunneling current. The mechanism of the etching process is proposed on the basis that the tunneling of electrons occurs directly from the valence band of the silicon electrode into the empty stares at the tip, leading to a hole injection in the silicon surface, followed by an electrochemical oxidation on the local surface underneath the tip.