  We present measurements of [Fe/H] for six M supergiant stars and three giant
stars within 0.5 pc of the Galactic Center (GC) and one M supergiant star
within 30 pc of the GC. The results are based on high-resolution (lambda /
Delta lambda =40,000) K-band spectra, taken with CSHELL at the NASA Infrared
Telescope Facility.We determine the iron abundance by detailed abundance
analysis,performed with the spectral synthesis program MOOG.The mean [Fe/H] of
the GC stars is determined to be near solar,[Fe/H] = +0.12 $\pm$ 0.22. Our
analysis is a differential analysis, as we have observed and applied the same
analysis technique to eleven cool, luminous stars in the solar neighborhood
with similar temperatures and luminosities as the GC stars. The mean [Fe/H] of
the solar neighborhood comparison stars, [Fe/H] = +0.03 $\pm$ 0.16, is similar
to that of the GC stars. The width of the GC [Fe/H] distribution is found to be
narrower than the width of the [Fe/H] distribution of Baade's Window in the
bulge but consistent with the width of the [Fe/H] distribution of giant and
supergiant stars in the solar neighborhood.
