Molecular electronic devices require at least two electrical contacts to one (or more) molecule(s). Single molecules are reliably probed by bonding one end to a gold substrate and the other end to a gold nanocrystal. The circuit is completed with a gold-coated atomic force microscope probe. Measurements of the decay of electronic current with the length of n-alkanedithiol molecules in these single-molecule nanojunctions are reported as a function of the applied bias. The value of the decay constant near zero bias was obtained from measurements in the ohmic region of the current-voltage curves. The electron tunneling decay rate is significantly smaller (βN = 0.57 ± 0.03) than observed for molecules bonded at just one end (βN ≈ 1), and it falls to even smaller values as the applied bias is increased. Both these effects are quantitatively accounted for by a large shift in molecular levels caused by the attachment of wires at each end.