We report a large kinetic isotope effect (KIE) for intramolecular charge transport through pi-conjugated oligophenylene imine (OPI) molecules > 4 nm in length connected to Au electrodes. 13C and 15N heavy-atom substitution on the imine bonds produces a normalized conductance KIE of ~2.7 per labeled atom in OPI wires, far larger than typical heavy-atom KIEs reported for chemical reactions. In contrast, isotopic labeling of the imine bonds for short OPI wires < 4 nm does not produce a conductance KIE, consistent with a direct tunneling mechanism expected for short molecules. Temperature dependent measurements on a long (> 4 nm) 15N-substituted OPI wire and its unlabeled isotopologue reveal that conductance is activated. The conductance results for long wires are thus consistent with multi-step polaron transport and we propose that the exceptionally large conductance KIEs imply a thermally-assisted, through-barrier polaron tunneling mechanism. In general, the observation of large heavy-atom conductance KIEs opens up considerable opportunities for exploring microscopic conduction mechanisms in pi-conjugated molecules.