  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.
