Fluorous liquids are the least polarizable condensed phases known, and their nonpolar members form solutions with conditions the closest to being in vacuo. A soluble salt consisting of a large fluorophilic anion, tetrakis[3,5-bis(perfluorohexyl)phenyl]borate, and its counterion, tetra-n-butylammonium, dissolved in perfluoromethylcyclohexane produces ionic solutions with extremely low conductivity. These solutions were subjected to small-angle neutron scattering (SANS) to ascertain the solute structure. At concentrations of 9% mass fraction, the fluorophilic electrolyte forms straight, long (>160 Å) self-assembled structures that are, in essence, long, homogeneous cylinders. Molecular models were made assuming a requirement for electroneutrality on the shortest length scale possible. This shows a structure formed from a stack of alternating anions and cations, and the structures fit the experimental scattering well. At the lower concentration of 1%, the stacks of ion pairs are shorter and eventually break up to form solitary ion pairs in the solution. These characteristics suggest such conditions provide an interesting new way to form long, self-assembling ionic nanostructures with single-molecule diameters in free solution onto which various moieties could be attached.