The dependence of the anisotropic chemical shift of Xe-129 trapped in the one-dimensional pores of the molecular sieve ALPO-11 was measured as a function of xenon loading. The anisotropy is axially symmetric and positive at low loading and then loses its axial symmetry with increased loading. An axial line shape is observed once again with increased loading, this time with the sign reversed from the previous time, with nonaxial line shapes at intermediate and high loadings. Two principal components of the observed shielding tenser vary linearly with Xe loading, and the third is invariant. All this behavior of the Line shape is analyzed in terms of a statistical distribution of three types of xenon sites (which have either 0, 1, or 2 neighboring sites occupied by other Xe, i.e., OXeO, XeXeO or XeXeXe), each with its characteristic shielding tenser, with fast exchange of the three site types at room temperature.