The Las Campanas Infrared Survey, based on broadband optical and near-infrared photometry, is designed to robustly identify a statistically significant and representative sample of evolved galaxies at redshifts z > 1. We have completed an H-band imaging survey over 1.1 deg(2) of sky in six separate fields. The average 5 sigma detection limit in a 4" diameter aperture is H similar to 20.8. Here we describe the design of the survey, the observation strategies, data-reduction techniques, and object identification procedures. We present sample near-infrared and optical photometric catalogs for objects identified in two survey fields. The optical images of the Hubble Deep Field South region obtained from the literature reach 5sigma detection thresholds in a 4" diameter aperture of U similar to 24.6, B similar to 26.1, V similar to 25.6, R similar to 25.1, and I similar to 24.2 mag. The optical images of the Chandra Deep Field South region obtained from our own observations reach 5sigma detection thresholds in a 4" diameter aperture of U similar to 26.8, R similar to 26.2, I similar to 25.3, and z' similar to 23.7 mag. We perform object detection in all bandpasses and identify greater than or similar to54,000 galaxies over 1408 arcmin(2) of sky in the two fields. Of these galaxies, 14,000 are detected in the H band and 2000 have the colors of evolved galaxies, I-H greater than or similar to 3, at z less than or similar to 1. We find that (1) the differential number counts N(m) for the H-band detected objects has a slope of d log N(m)/dm = 0.45 +/- 0.01 mag(-2) at H less than or similar to 19 and 0.27 +/- 0.01 mag(-2) at H greater than or similar to 19, with a mean surface density approximate to7200 deg(-2) mag(-1) at H = 19. In addition, we find that (2) the differential number counts for the H-band-detected red objects has a very steep slope, d log N(m; I-H greater than or similar to 3)/dm = 0.84 +/- 0.06 mag(-2) at H less than or similar to 20 and 0.32 +/- 0.07 mag(-2) at H greater than or similar to 20, with a mean surface density approximate to3000 deg(-2) mag(-1) at H = 20. Finally, we find that (3) galaxies with red optical to near-IR colors (I-H > 3) constitute approximate to20% of the H-band-detected galaxies at H less than or similar to 21, but only approximate to2% at H less than or similar to 19. We show that red galaxies are strongly clustered, which results in a strong field-to-field variation in their surface density. Comparisons of observations and predictions based on various formation scenarios indicate that these red galaxies are consistent with mildly evolving early-type galaxies at z similar to 1, although with a significant amount of ongoing star formation, as indicated by the large scatter in their V-I colors.