The oxygen and hydrogen isotopic composition in snow and ice have long been utilized to reconstruct past temperatures of polar regions, under the assumption that post-depositional processes such as sublimation do not fractionate snow. In low-accumulation (<0.01 m yr-1) areas near the McMurdo Dry Valleys in Antarctica surface snow and ice samples have negative deuterium excess values (δD - 8*δ18O). This unique phenomenon, only observed near the Dry Valleys, is not fully understood. Here we use both an isotope-enabled general circulation model and an ice physics model and establish that negative deuterium excess values can only arise from precipitation if the majority of the moisture is sourced from the Southern Ocean. However, the model results show that moisture sourced from oceans north of 55°S contributes significantly (>50%) to precipitation in Antarctica today. We thus propose that sublimation must have occurred to yield the negative deuterium excess values in snow observed in and near the Dry Valleys and that solid-phase-diffusion in ice grains is sufficiently fast to allow Rayleigh-like isotopic fractionation in similar environments. We calculate that under present-day conditions at the Allan Hills outside the Dry Valleys, 3 to 24% of the surface snow is lost due to sublimation. Because a higher fraction of snow is expected to be sublimed when accumulation rates are lower, the magnitude of δ18O and δD enrichment due to sublimation will be higher during past cold periods than at present, altering the relationship between the snow isotopic composition and polar temperatures.