The Sloan Digital Sky Survey III's Apache Point Observatory Galactic Evolution Experiment (APOGEE) is a high-resolution near-infrared spectroscopic survey covering all of the major components of the Galaxy, including the dust-obscured regions of the inner Milky Way disk and bulge. Here we present a sample of 10,341 likely red-clump stars (RC) from the first two years of APOGEE operations, selected based on their position in color-metallicity-surface-gravity-effective-temperature space using a new method calibrated using stellar evolution models and high-quality asteroseismology data. The narrowness of the RC locus in color-metallicity-luminosity space allows us to assign distances to the stars with an accuracy of 5%-10%. The sample extends to typical distances of about 3 kpc from the Sun, with some stars out to 8 kpc, and spans a volume of approximately 100 kpc3 over 5 kpc <~ R <~ 14 kpc, |Z| <~ 2 kpc, and –15° <~ Galactocentric azimuth <~ 30°. The APOGEE red-clump (APOGEE-RC) catalog contains photometry from the Two Micron All Sky Survey, reddening estimates, distances, line-of-sight velocities, stellar parameters and elemental abundances determined from the high-resolution APOGEE spectra, and matches to major proper motion catalogs. We determine the survey selection function for this data set and discuss how the RC selection samples the underlying stellar populations. We use this sample to limit any azimuthal variations in the median metallicity within the ≈45° azimuthal region covered by the current sample to be <=0.02 dex, which is more than an order of magnitude smaller than the radial metallicity gradient. This result constrains coherent non-axisymmetric flows within a few kiloparsecs from the Sun.