Relativistic contributions to the chemical shift of Xe-129 in Xe@C-60 have been computed by means of a two-component relativistic density functional approach. It is demonstrated that in all-electron calculations the scalar relativistic effects are moderate, of the order of 20 ppm depending on the basis set used, and tend to increase the chemical shift. The spin-orbit coupling induced contributions are small (a few ppm) and negative in all but two cases. The basis set dependence of the results is pronounced. In contrast to nonrelativistic Hartree-Fock studies of Xe@C-60, which strongly underestimate the experimental value of 179.24 ppm with respect to Xe gas, [61-72 ppm, Chem. Phys. Lett. 1997, 275, 14; 103 ppm, present work], our DFT results systematically overestimate the xenon shift (relativistically, greater than or equal to246 ppm). The large difference between the present nonrelativistic DFT results and the Hartree-Fock data can serve as an estimate of the important contributions due to electron correlation. Compared to the chemical shift range of Xe-129 (7000 ppm) the chemical shift in Xe@C-60 is not large, and sizable relative errors can therefore be expected from currently feasible computations. Many comparatively small effects, with opposite signs, contribute to the final result and must therefore not be neglected.