A series of thioacetate-terminated butadiyne-linked porphyrin oligomers have been synthesized with one to three porphyrin repeat units. Single molecule electrical scanning tunneling microscopy measurements using the I(s) and I(t) methods were used to determine the molecule conductances for this series of oligomers. The molecular conductance shows an exponential falloff with sulfur-sulfur distance with a remarkably low attenuation factor of beta = (0.04 +/- 0.006) A-1.