We report on studies of an inorganic electrolyte: LiAlCl4 in liquid sulfur dioxide. Concentrated solutions show a very high conductivity when compared with typical electrolytes for lithium ion batteries that are based on organic solvents. Our investigations include conductivity measurements and measurements of transference numbers via nuclear magnetic resonance (NMR) and by a classical direct method, Hittorf's method. For the use of Hittorf's method, it is necessary to measure the concentration of the electrolyte in a selected cell compartment before and after electrochemical polarization very precisely. This task was finally performed by potentiometric titration after hydrolysis of the salt. The Haven ratio was determined to estimate the association behavior of this very concentrated electrolyte solution. The measured unusually high transference number of the lithium cation of the studied most concentrated solution, a molten solvate LiAlCl4 x 1.6SO(2), makes this electrolyte a promising alternative for lithium ion cells with high power ability.