We present chemical abundances in a sample of luminous cool stars located within 30 pc of the Galactic Center. Abundances of carbon, nitrogen, oxygen, calcium, and iron were derived from high-resolution infrared spectra in the H- and K-bands. The abundance results indicate that both [O/Fe] and [Ca/Fe] are enhanced respectively by averages of +0.2 and +0.3 dex, relative to either the Sun or the Milky Way disk at near solar Fe abundances. The Galactic Center stars show a nearly uniform and nearly solar iron abundance. The mean value of A(Fe) = 7.59 +/- 0.06 agrees well with previous work. The total range in Fe abundance among Galactic Center stars, 0.16 dex, is significantly narrower than the iron abundance distributions found in the literature for the older bulge population. Our snapshot of the current-day Fe abundance within 30 pc of the Galactic Center samples stars with an age less than 1 Gyr; a larger sample in time (or space) may find a wider spread in abundances.