Iodine added to iodide-based ionic liquids leads to extraordinarily efficient charge transport, vastly exceeding that expected for such viscous systems. Using terahertz time-domain spectroscopy, in conjunction with dc conductivity, diffusivity and viscosity measurements we unravel the conductivity pathways in 1-methyl-3-propylimidazolium iodide melts. This study presents evidence of the Grotthuss mechanism as a significant contributor to the conductivity, and provides new insights into ion pairing processes as well as the formation of polyiodides. The terahertz and transport results are reunited in a model providing a quantitative description of the conduction by physical diffusion and the Grotthuss bond-exchange process. These novel results are important for the fundamental understanding of conduction in molten salts and for applications where ionic liquids are used as charge-transporting media such as in batteries and dye-sensitized solar cells.