The single-molecule conductivity of quinone-oligo(phenylene vinylene) (Q-OPV) attached to a gold substrate was studied using electrochemical scanning tunnelling microscopy. The results show that the molecule has two discrete conductivity states: a low-conductivity state, when it is oxidized, and a high-conductivity state, when reduced. The electron transport through the molecule in both states occurs via coherent tunnelling. The molecular conductivity in either oxidation state is independent from the electrochemical gate potential; however, the gate potential can be used to switch the oxidation state of the molecule. Numerical calculations suggest that the highest occupied molecular orbital (HOMO) of Q-OPV controls tunnelling through the molecule and that the independence of conductivity from the electrochemical gate in either oxidation state originates from strong penetration of HOMO into the substrate. In addition, the greater delocalization of HOMO in the reduced state than in the oxidized state explains the greater conductivity of Q-OPV in the former than in the latter.