We propose a new mechanism for diffusion of surface adsorbates in which motion of the substrate atoms to which the adsorbates are attached results in the motion of the substrate-adsorbate complex. We show an experimental example-the motion of self-assembled monolayers of CH3O2C(CH2)(15)SH on gold which we have observed by time-lapse imaging using scanning tunneling microscopy. This mechanism is also used to explain previous data for motion of Cu-O complexes on the Cu{110} surface.