The search for long molecular wires that can transport charge with maximum efficiency over many nanometers has driven molecular electronics since its inception. Single-molecule conductance normally decays with length and is typically far below the theoretical limit of G0 (77.5 μS). Here, we measure the conductances of a family of edge-fused porphyrin ribbons (lengths 1-7 nm) that display remarkable behavior. The low-bias conductance is high across the whole series. Charging the molecules in situ results in a dramatic realignment of the frontier orbitals, increasing the conductance to 1 G0 (corresponding to a current of 20 μA). This behavior is most pronounced in the longer molecules due to their smaller HOMO-LUMO gaps. The conductance-voltage traces frequently exhibit peaks at zero bias, showing that a molecular energy level is in resonance with the Fermi level. This work lays the foundations for long, perfectly transmissive, molecular wires with technological potential.