We report the confirmation and characterization of a transiting gas giant planet orbiting the M dwarf KOI-254 every 2.455239 days, which was originally discovered by the Kepler mission. We use radial velocity measurements, adaptive optics imaging, and near-infrared spectroscopy to confirm the planetary nature of the transit events. KOI-254 b is the first hot Jupiter discovered around an M-type dwarf star. We also present a new model-independent method of using broadband photometry to estimate the mass and metallicity of an M dwarf without relying on a direct distance measurement. Included in this methodology is a new photometric metallicity calibration based on J-K colors. We use this technique to measure the physical properties of KOI-254 and its planet. We measure a planet mass of M sub(P) = 0.505 M sub(Jup), radius R sub(P) = 0.96 R sub(Jup), and semimajor axis a = 0.030 AU, based on our measured stellar mass Mlow * = 0.59 M sub((.)) and radius Rlow * = 0.55 R sub((.)). We also find that the host star is metal-rich, which is consistent with the sample of M-type stars known to harbor giant planets.