We report, for the first time, a calculation of the isotropic NMR chemical shift of Xe-129 in the cages of clathrate hydrates Structures I and II. We generate a shielding surface for Xe in the clathrate cages by quantum mechanical calculations. Subsequently this shielding surface is employed in canonical Monte Carlo simulations to find the average isotropic Xe shielding values in the various cages. For the two types of cages in clathrate hydrate Structure I, we find the intermolecular shielding values [sigma(Xe@5(12) cage)-sigma(Xe atom)]=-214.0 ppm, and [sigma(Xe@5(12)6(2) cage)-sigma(Xe atom)]=-146.9 ppm, in reasonable agreement with the values -242 and -152 ppm, respectively, observed experimentally by Ripmeester and co-workers between 263 and 293 K. For the 5(12) and 5(12)6(4) cages of Structure II we find [sigma(Xe@5(12) cage)-sigma(Xe atom)]=-206.7 ppm, and [sigma(Xe@5(12)6(4) cage)-sigma(Xe atom)]=-104.7 ppm, also in reasonable agreement with the values -225 and -80 ppm, respectively, measured in a Xe-propane type II mixed clathrate hydrate at 77 and 220-240 K by Ripmeester (C) 2004 American Institute of Physics.