We present a single-molecule study demonstrating that resonant charge transport through vibronic states takes place in molecules that are strongly anchored at an electrode. The molecules are adsorbed on a CuN/Cu(100) surface, with the molecular terminal group attaching to the Cu ridge. We use a scanning tunneling microscope to inject charges into the highest occupied molecular orbital and excite vibronic transitions. The charges are then transferred in a single-electron process through either a single or a double intramolecular channel, depending on molecular adsorption configuration. These phenomena are explained in terms of localized molecular orbitals and an effective intramolecular barrier.