The phase diagram of the redox active ionic liquid 1-methyl-3-propylimidazolium iodide (PMII) is examined as a function of temperature and iodine concentration. Beyond a threshold concentration of 3.9 M, the formation of higher polyiodides gives rise to a viscoelastic phase upon cooling. Despite of the very high viscosity of such polyiodide-containing PMII melts a strikingly high conductivity is maintained through Grotthuss-type bond exchange and ionic conduction.