We report here the discovery of the first planet around an ultracool dwarf star. It is also the first extrasolar giant planet astrometrically discovered around a main-sequence star. The statistical significance of the detection is shown in two ways. First, there is a 2 × 10^–8 probability that the astrometric motion fits a parallax-and-proper-motion-only model. Second, periodogram analysis shows a false alarm probability of 3 × 10^–5 that the discovered period is randomly generated. The planetary mass is M ₂ = 6.4 (+2.6,–3.1) Jupiter-masses (M _J), and the orbital period is P = 0.744 (+0.013,–0.008) yr in the most likely model. In less likely models, companion masses that are higher than the 13 M _J planetary mass limit are ruled out by past radial velocity (RV) measurements unless the system RV is more than twice the current upper limits and the near-periastron orbital phase was never observed. This new planetary system is remarkable, in part, because its star, VB 10, is near the lower mass limit for a star. Our astrometric observations provide a dynamical mass measurement and will in time allow us to confront the theoretical models of formation and evolution of such systems and their members. We thus add to the diversity of planetary systems and to the small number of known M-dwarf planets. Planets such as VB 10b could be the most numerous type of planets because M stars comprise >70% of all stars. To date they have remained hidden since the dominant RV planet-discovery technique is relatively insensitive to these dim, red systems.