We describe the Carnegie-Spitzer-IMACS (CSI) Survey, a wide-field, near-IR selected spectrophotometric redshift survey with the Inamori Magellan Areal Camera and Spectrograph (IMACS) on Magellan-Baade. By defining a flux-limited sample of galaxies in Spitzer 3.6micron imaging of SWIRE fields, the CSI Survey efficiently traces the stellar mass of average galaxies to z~1.5. This first paper provides an overview of the survey selection, observations, processing of the photometry and spectrophotometry. We also describe the processing of the data: new methods of fitting synthetic templates of spectral energy distributions 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 37,000 high quality redshifts in our first 5.3 sq.degs of the SWIRE XMM-LSS field. We use three different approaches to estimate our redshift errors and find robust agreement. Over the full range of 3.6micron fluxes of our selection, we find typical uncertainties of sigma_z/(1+z) < 0.015. In comparisons with previously published VVDS redshifts, for example, we find a scatter of sigma_z/(1+z) = 0.012 for galaxies at 0.8< z< 1.2. For galaxies brighter and fainter than i=23 mag, we find sigma_z/(1+z) = 0.009 and sigma_z/(1+z) = 0.025, 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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