We describe the Carnegie-Spitzer-IMACS (CSI) Survey, a wide-field, near-IR selected spectrophotometric redshift survey with IMACS on Magellan-Baade. CSI uses a flux-limited sample of galaxies in Spitzer IRAC 3.6micron imaging of SWIRE fields to efficiently trace the stellar mass of average galaxies to z~1.5. This paper provides an overview of the survey selection, observations, and processing of the photometry and spectrophotometry. We also describe the analysis of the data: new methods of fitting synthetic SEDs are used to derive redshifts, stellar masses, emission line luminosities, and coarse information on recent star-formation. Our unique methodology for analyzing low-dispersion spectra taken with multilayer prisms in IMACS, combined with panchromatic photometry from the ultraviolet to the IR, has yielded high quality redshifts for 43,347 galaxies in our first 5.3 sq. degs of the SWIRE XMM-LSS field. A new approach to assessing data quality is also described, and three different approaches are used to estimate our redshift errors, with robust agreement. Over the full range of 3.6micron fluxes of our selection, we find typical redshift uncertainties of sigma_z/(1+z) < 0.015. In comparisons with previously published spectroscopic redshifts we find scatters of sigma_z/(1+z) = 0.011 for galaxies at 0.7< z< 0.9, and sigma_z/(1+z) = 0.014 for galaxies at 0.9< z< 1.2. For galaxies brighter and fainter than i=23 mag, we find sigma_z/(1+z) = 0.008 and sigma_z/(1+z) = 0.022, respectively. Notably, our low-dispersion spectroscopy and analysis yields comparable redshift uncertainties and success rates for both red and blue galaxies, largely eliminating color-based systematics that can seriously bias observed dependencies of galaxy evolution on environment.
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