The low infrared background and high atmospheric transparency are the principal advantages of Antarctic Plateau sites for astronomy. However, the poor seeing (between 1 and 3 as) negates much of the sensitivity improvements that the Antarctic atmosphere offers, compared to mid-latitude sites such as Mauna Kea or Cerro Paranal. The seeing at mid-latitude sites, though smaller in amplitude, is dominated by turbulence at altitudes of 10–20 km. Over the Antarctic Plateau, virtually no high altitude turbulence is present in the winter. The mean square error for an astrometric measurement with a dual-beam, differential astrometric interferometer in the very narrow angle regime is proportional to the integral of h2C2N(h). Therefore, sites at which the turbulence occurs only at low altitudes offer large gains in astrometric precision. We show that a modest interferometer at the South Pole can achieve 10 μ as differential astrometry 300 times faster than a comparable interferometer at a good mid-latitude site, in median conditions. Science programs that would benefit from such an instrument include planet detection and orbit determination, and astrometric observation of stars microlensed by dark matter candidates.