Significance: The measured electronic properties of proteins are known to depend critically on contacts, although little is known at the single-molecule level. Here, we have measured the conductance of single-protein molecules in their natural aqueous environment, but in conditions where no ion current flows, finding large conductances (nanosiemens) over long paths (many nanometers) when the protein is tethered by chemical contacts formed by binding-specific ligands. This provides a method for forming reliable contacts to proteins, and for the specific detection of single molecules. Thus, single antibodies, such as anti-Ebola IgG, can be detected electrically when they bind a peptide epitope tethered to electrodes, with no background signal from molecules that do not bind specifically.