Multi-heme cytochromes (MHCs) are fascinating proteins used by bacterial organisms to shuttle electrons within, between, and out of their cells. When placed in solid-state electronic junctions, MHCs support temperature-independent currents over several nanometers that are 3 orders of magnitude higher compared to other redox proteins of similar size. To gain molecular-level insight into their astonishingly high conductivities, we combine experimental photoemission spectroscopy with DFT+Σ current-voltage calculations on a representative Gold-MHC-Gold junction. We find that conduction across the dry, 3 nm long protein occurs via off-resonant coherent tunneling, mediated by a large number of protein valence-band orbitals that are strongly delocalized over heme and protein residues. This picture is profoundly different from the electron hopping mechanism induced electrochemically or photochemically under aqueous conditions. Our results imply that the current output in solid-state junctions can be even further increased in resonance, for example, by applying a gate voltage, thus allowing a quantum jump for next-generation bionanoelectronic devices.