We have spatially resolved the electronic penetration of metallic electronic states through a molecular wire connected to an atomically clean contact. The molecular wire, which is 0.3 nm wide and 1.7 nm long, was electronically connected on one side, and a scanning tunneling microscope tip was used as a second movable electronic counterelectrode. The results reveal a clear exponential decay in the transparency (conductance) of the wire with distance from the contacted end. Analysis of the data shows that electrons are transported along the molecular wire by virtual resonance tunneling with an inverse decay length of 4 nm-1, in excellent agreement with theoretical calculations.