  We describe the algorithm used to select the Luminous Red Galaxy (LRG) sample
for the extended Baryon Oscillation Spectroscopic Survey (eBOSS) of the Sloan
Digital Sky Survey IV (SDSS-IV) using photometric data from both the SDSS and
the Wide-Field Infrared Survey Explorer (WISE). LRG targets are required to
meet a set of color selection criteria and have z-band and i-band MODEL
magnitudes z < 19.95 and 19.9 < i < 21.8, respectively. Our algorithm selects
roughly 50 LRG targets per square degree, the great majority of which lie in
the redshift range 0.6 < z < 1.0 (median redshift 0.71). We demonstrate that
our methods are highly effective at eliminating stellar contamination and
lower-redshift galaxies. We perform a number of tests using spectroscopic data
from SDSS-III/BOSS to determine the redshift reliability of our target
selection and its ability to meet the science requirements of eBOSS. The SDSS
spectra are of high enough signal-to-noise ratio that at least 89% of the
target sample yields secure redshift measurements. We also present tests of the
uniformity and homogeneity of the sample, demonstrating that it should be clean
enough for studies of the large-scale structure of the universe at higher
redshifts than SDSS-III/BOSS LRGs reached.
