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 σ detection limit in a 4" diameter aperture is H ~ 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 5 σ detection thresholds in a 4" diameter aperture of U ~ 24.6, B ~ 26.1, V ~ 25.6, R ~ 25.1, and I ~ 24.2 mag. The optical images of the Chandra Deep Field-South region obtained from our own observations reach 5 σ detection thresholds in a 4" diameter aperture of V ~ 26.8, R ~ 26.2, I ~ 25.3, and z' ~ 23.7 mag. We perform object detection in all bandpasses and identify ≳ 54,000 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 ≳ 3, at z ≳ 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 ≾ 19 and 0.27 ± 0.01 mag^(-2) at H ≳ 19, with a mean surface density ≈7200 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 ≳ 3)/dm = 0.84 ± 0.06 mag^(-2) at H ≾ 20 and 0.32 ± 0.07 mag^(-2) at H ≳ 20, with a mean surface density ≈3000 deg^(-2) mag^(-1) at H = 20. Finally, we find that (3) galaxies with red optical to near-IR colors (I-H > 3) constitute ≈20% of the H-band-detected galaxies at H ≾ 21, but only ≈2% at H ≾ 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 ~ 1, although with a significant amount of ongoing star formation, as indicated by the large scatter in their V-I colors.