We present new near-infrared data and an analysis which indicates that the ``Pistol Star'' is one of the most luminous stars known, adding another test point for massive star formation and stellar evolution theories. We estimate an extinction of AK = 3.2+/-0.5 using the near-infrared colors of the star and surrounding stars in the young Quintuplet cluster. Using our wind/atmosphere code, we find two families of models which fit the spectral energy distribution and detailed line profiles. The lower luminosity models give L = 106.6+/-0.2 Lsun and Teff = 104.15+/-0.01 K, while the higher luminosity models give L = 107.2+/-0.2 Lsun and Teff = 104.33+/-0.01 K; the error in luminosity assumes an uncertainty of +/-0.5 in AK, while the error in Teff is constrained by detailed line modeling. The models also reveal a helium enriched surface. As previously existing stellar evolution models do not extend to such high luminosities, we employ new evolutionary tracks for very massive stars to determine the initial mass and age of the Pistol Star, and estimate M_initial = 200-250 Msun and an age of 1.7-2.1 Myrs. The inferred luminosity and temperature place the star in a sparsely populated zone in the HR diagram where ``Luminous Blue Variables'' (LBVs) are often found. This is consistent with our evolutionary models which predict that the star is in an unstable evolutionary stage. We interpret the star and its surrounding nebula as an LBV which has recently ejected large amounts of material. Our K-band speckle imaging data reveal the star to be single down to a projected separation of 110 AU.