Proteins are widely regarded as insulators, despite reports of electrical conductivity. Here we use measurements of single proteins between electrodes, in their natural aqueous environment to show that the factor controlling measured conductance is the nature of the electrical contact to the protein, and that specific ligands make highly selective electrical contacts. Using six proteins that lack known electrochemical activity, and measuring in a potential region where no ion current flows, we find characteristic peaks in the distributions of measured single-molecule conductances. These peaks depend on the contact chemistry, and hence, on the current path through the protein. In consequence, the measured conductance distribution is sensitive to changes in this path caused by ligand binding, as shown with streptavidin–biotin complexes. Measured conductances are on the order of nanosiemens over distances of many nanometers, orders of magnitude more than could be accounted for by electron tunneling. The current is dominated by contact resistance, so the conductance for a given path is independent of the distance between electrodes, as long as the contact points on the protein can span the gap between electrodes. While there is no currently known biological role for high electronic conductance, its dependence on specific contacts has important technological implications, because no current is observed at all without at least one strongly bonded contact, so direct electrical detection is a highly selective and label-free single-molecule detection method. We demonstrate single-molecule, highly specific, label- and background free-electronic detection of IgG antibodies to HIV and Ebola viruses.