Salts of the small symmetrical guanidinium cation, which are important protein denaturants in biophysical chemistry, are studied in the ionic liquid state for the first time. Their conductivities prove to be among the highest measured, and their liquid fragilities prove exceptional. We link these features to the large number of exchangeable protons per cation. We present evidence that the unusual properties stem from the increasing delocalization of protons among alternative structural moieties under increasing thermal excitation, and from the associated increase in "dry" proton contribution to the mass transport properties.