An X-ray diffraction single crystal study of Cs1.5Li1.5H(SO4)2 has been performed, with the aim of determining the atomic structure and possible pathways of proton transport in this compound. M(r) = 402.90, lambda(Mo Kalpha) = 0.70930 angstrom, cubic, I4BAR 3d, a = 11.693 (1) angstrom, V = 1599.0 (3) angstrom3, Z= 8, D(x) = 3.35 g.cm-3, mu = 74.9 cm-1. F(000) = 1472, room temperature, R(F) = 0.017, R(F)w = 0.018 for 394 unique reflections. The high protonic conductivity of Cs1.5Li1.5H(SO4)2 is due to a dynamically disordered hydrogen bond network (DDHBN), which exists in the crystal structure even at room temperature. The "principal proton transport" occurs within the framework of the hydrogen bonded chains and is, therefore, essentially one-dimensional.