The metal-reducing bacterium Geobacter sulfurreducens produces conductive protein appendages known as "pilus nanowires" to transfer electrons to metal oxides and to other cells. These processes can be harnessed for the bioremediation of toxic metals and the generation of electricity in bioelectrochemical cells. Key to these applications is a detailed understanding of how these nanostructures conduct electrons. However, to the best of our knowledge, their mechanism of electron transport is not known. We used the capability of scanning tunneling microscopy (STM) to probe conductive materials with higher spatial resolution than other scanning probe methods to gain insights into the transversal electronic behavior of native, cell-anchored pili. Despite the presence of insulating cellular components, the STM topography resolved electronic molecular substructures with periodicities similar to those reported for the pilus shaft. STM spectroscopy revealed electronic states near the Fermi level, consistent with a conducting material, but did not reveal electronic states expected for cytochromes. Furthermore, the transversal conductance was asymmetric, as previously reported for assemblies of helical peptides. Our results thus indicate that the Geobacter pilus shaft has an intrinsic electronic structure that could play a role in charge transport.