The electron transfer properties of proteins are normally measured as molecularly averaged ensembles. Through these and related measurements, proteins are widely regarded as macroscopically insulating materials. Using scanning tunnelling microscopy (STM), we present new measurements of the conductance through single-molecules of the electron transfer protein cytochrome b(562) in its native conformation, under pseudo-physiological conditions. This is achieved by thiol (SH) linker pairs at opposite ends of the molecule through protein engineering, resulting in defined covalent contact between a gold surface and a platinum-iridium STM tip. Two different orientations of the linkers were examined: a long-axis configuration (SH-LA) and a short-axis configuration (SH-SA). In each case, the molecular conductance could be 'gated' through electrochemical control of the heme redox state. Reproducible and remarkably high conductance was observed in this relatively complex electron transfer system, with single-molecule conductance values peaking around 18 nS and 12 nS for the SH-SA and SH-LA cytochrome b(562) molecules near zero electrochemical overpotential. This strongly points to the important role of the heme co-factor bound to the natively structured protein. We suggest that the two-step model of protein electron transfer in the STM geometry requires a multi-electron transfer to explain such a high conductance. The model also yields a low value for the reorganisation energy, implying that solvent reorganisation is largely absent.