We report 1."9/300 km s-1 resolution imaging spectroscopy of He I n = 2(1)P --> n = 2(1)S 2.06-mu-m line emission in the Galactic center. There is a group of about a dozen compact, broad-line "He i emission-line stars" most of which are positionally coincident with compact 2-mu-m continuum sources. IRS 16 and its "broad-line region" is probably a central concentration of this 1 pc diameter He I star cluster. The He I stars may be blue supergiants with heavy mass loss. The high He I/H I (Br-alpha, Br-gamma) ratios suggest an overabundance of helium in their atmospheres indicative of a post-main-sequence phase. Mass-loss rates may range between a few 10(-5) and 10(-4) M. yr-1, and outflow velocities are between 500 and 1000 km s-1. The He I stars are members of a cluster of massive stars that can very likely account for the entire luminosity, the flux of Lyman-continuum photons, and the fairly low excitation of the central few parsecs. Our data show very clearly that massive star formation has taken place in the Galactic center within the last few 10(6) yr.