Organic molecules can self-assemble into well-ordered structures, but the conductance of these structures is limited(1-3), which is a disadvantage for applications in molecular electronics. Conductivity can be improved by using coordination polymers-in which metal centres are incorporated into a molecular backbone-and such structures have been used as molecular wires by self-assembling them into ordered films on metal surfaces(4). Here, we report electrically conductive nanoribbons of the coordination polymer [Pt2I(S2CCH3)(4)](n) self-assembled on an insulating substrate by direct sublimation of polymer crystals. Conductance atomic force microscopy is used to probe the electrical characteristics of a few polymer chains (similar to 10) within the nanoribbons. The observed currents exceed those previously sustained in organic and metal-organic molecules assembled on surfaces by several orders of magnitude and over much longer distances. These results, and the results of theoretical calculations based on density functional theory, confirm coordination polymers as candidate materials for applications in molecular electronics.