Here we describe the combination of an archetypal redox-active metal sulfide cluster, Fe4S4, with an organic linker, 1,4-benzenedithiolate, to prepare coordination polymers containing infinite chains of Fe4S4 clusters. The crystal structures of two solid materials have been solved from synchrotron X-ray powder diffraction data using simulated annealing and refined by a least-squares Rietveld refinement procedure. The electronic properties of these chains have also been characterized by UV-visible and Mössbauer spectroscopies. Additional experiments demonstrated that these chains can be solubilized by variation of the countercation and that the chain structure is maintained in solution. The redox-activity of the Fe4S4 clusters can be accessed with chemical reagents. Introduction of charge carriers by reduction of the Fe4S4 clusters is found to increase the electrical conductivity of the materials by up to 4 orders of magnitude. These results highlight the utility of Fe4S4 clusters as redox-active building blocks in preparing new classes of coordination polymers.