Proteins are commonly known to transfer electrons over distances limited to a few nanometers. However, many biological processes require electron transport over far longer distances. For example, soil and sediment bacteria transport electrons, over hundreds of micrometers to even centimeters, via putative filamentous proteins rich in aromatic residues. However, measurements of true protein conductivity have been hampered by artifacts due to large contact resistances between proteins and electrodes. Using individual amyloid protein crystals with atomic-resolution structures as a model system, we perform contact-free measurements of intrinsic electronic conductivity using a four-electrode approach. We find hole transport through micrometer-long stacked tyrosines at physiologically relevant potentials. Notably, the transport rate through tyrosines (105 s-1) is comparable to cytochromes. Our studies therefore show that amyloid proteins can efficiently transport charges, under ordinary thermal conditions, without any need for redox-active metal cofactors, large driving force, or photosensitizers to generate a high oxidation state for charge injection. By measuring conductivity as a function of molecular length, voltage, and temperature, while eliminating the dominant contribution of contact resistances, we show that a multistep hopping mechanism (composed of multiple tunneling steps), not single-step tunneling, explains the measured conductivity. Combined experimental and computational studies reveal that proton-coupled electron transfer confers conductivity; both the energetics of the proton acceptor, a neighboring glutamine, and its proximity to tyrosine influence the hole transport rate through a proton rocking mechanism. Surprisingly, conductivity increases 200-fold upon cooling due to higher availability of the proton acceptor by increased hydrogen bonding.