We propose a novel mechanism for ion acceleration based on the guided motion of electrons from a thin layer. The electron motion is locked to the moving nodes of a standing wave formed by a chirped laser pulse reflected from a mirror behind the layer. This provides a stable longitudinal field of charge separation, thus giving rise to chirped-standing-wave acceleration of the residual ions of the layer. We demonstrate, both analytically and numerically, that stable proton beams, with energy spectra peaked around 100 MeV, are feasible for pulse energies at the level of 10 J. Moreover, a scaling law for higher laser intensities and layer densities is presented, indicating stable GeV-level energy gains of dense ion bunches, for soon-to-be-available laser intensities.