The average near-infrared (K-band) luminosity of 238 Hipparcos red clump giants is derived and then used to measure the distance to the Galactic center. These Hipparcos red clump giants have been previously employed as I-band standard candles. The advantage of the K-band is a decreased sensitivity to reddening, and perhaps also a reduced systematic dependence on metallicity. In order to investigate the latter, and also to refer our calibration to a known metallicity zero-point, we restrict our sample of red clump calibrators to those with abundances derived from high-resolution spectroscopic data. The mean metallicity of the sample is [Fe/H] = -0.18 dex. The data are consistent with no correlation between M_K and [Fe/H], and only weakly constrain the slope of this relation. The luminosity function of the sample peaks at M_K = -1.61 +- 0.03 mag. Next, we assemble published optical and near-infrared photometry for about 20 red clump giants in a Baade's Window field with a mean metallicity nearly identical to that of the Hipparcos red clump. We derive the distance to the Galactic center: R = 8.24 +- 0.42 kpc. The uncertainty in this distance measurement is dominated by the small number of Baade's Window red clump giants examined here [abridged].

Accepted to The Astrophysical Journal, 28 pages, 7 figures, 1 table