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 (beta(N) = 0.57+/-0.03) than observed for molecules bonded at just one end (beta(N)approximate to1), 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.