We present images of the Vega system obtained with the IRAM Plateau de Bure interferometer at a 1.3 mm wavelength with submillijansky sensitivity and ∼2.5 resolution (about 20 AU). These observations clearly detect the stellar photosphere and two dust emission peaks offset from the star by 9.5 and 8.0 to the northeast and southwest, respectively. These offset emission peaks are consistent with the barely resolved structure visible in previous submillimeter images, and they account for a large fraction of the dust emission. The presence of two dust concentrations at the observed locations is plausibly explained by the dynamical influence of an unseen planet of a few Jupiter masses in a highly eccentric orbit that traps dust in principal mean...