We present images of the Vega system obtained with the IRAM Plateau de Bure interferometer at 1.3 millimeters wavelength with sub-mJy sensitivity and $sim2farcs5$ resolution (about 20 AU). These observations clearly detect the stellar photosphere and two dust emission peaks offset from the star by $9farcs5$ and $8farcs0$ 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 principle mean motion resonances.