We present new infrared images, obtained with the Hubble Space Telescope (HST) Near-infrared Camera and Multi-object Spectrometer (NICMOS), and Br- alpha (4.05 micron ) spectroscopy, obtained using CGS4 on UKIRT, of the Pistol Star and its associated nebula. We find strong evidence to support the hypothesis that the Pistol Nebula was ejected from the Pistol Star. The Pa- alpha (1.87 micron ) NICMOS image shows that the nebula completely surrounds the Pistol Star, although the line intensity is much stronger on its northern and western edges. The Br- alpha CGS4 spectra show the classical ring-like signature of quasi-spherical expansion. The blueshifted emission (V_max ~ -60 km/sec ) is much weaker than the redshifted emission (V_max ~ +10 km/sec ), where the velocities are with respect to the velocity of the Pistol Star; further, the redshifted emission spans a very narrow range of velocities, i.e., it appears ``flattened'' in the position-velocity diagram. These data suggest that the nebula was ejected from the star several thousand years ago, with a velocity between the current terminal velocity of the stellar wind (95 km/sec ) and the present expansion velocity of gas in the outer shell of the nebula (60 km/sec ). The Pa- alpha image reveals several emission-line stars in the region, including two newly-identified emission-line stars north of the Pistol Star, both of which are likely to be the hottest known stars in the Galactic center with spectral types earlier than WC8 and T_eff > 50,000 K). The presence of these stars, the morphology of the Pa- alpha emission, and the velocity field in the gas suggest that the side of the nebula furthest from us is approaching, and being ionized by, the hot stars of the Quintuplet, and that the highest velocity redshifted gas has been decelerated by winds from the Quintuplet stars. We also discuss the possibility that the nebular gas might be magnetically confined by the ambient magnetic field delineated by the nearby nonthermal filaments.