We present a catalog of high-energy gamma-ray sources detected by the Large Area Telescope (LAT), the primary science instrument on the Fermi Gamma-ray Space Telescope (Fermi), during the first 11 months of the science phase of the mission, which began on 2008 August 4. The First Fermi-LAT catalog (1FGL) contains 1451 sources detected and characterized in the 100 MeV to 100 GeV range. Source detection was based on the average flux over the 11-month period, and the threshold likelihood Test Statistic is 25, corresponding to a significance of just over 4 sigma. The 1FGL catalog includes source location regions, defined in terms of elliptical fits to the 95% confidence regions and power-law spectral fits as well as flux measurements in 5 energy bands for each source. In addition, monthly light curves are provided. Using a protocol defined before launch we have tested for several populations of gamma-ray sources among the sources in the catalog. For individual LAT-detected sources we provide firm identifications or plausible associations with sources in other astronomical catalogs. Identifications are based on correlated variability with counterparts at other wavelengths, or on spin or orbital periodicity. For the catalogs and association criteria that we have selected, 630 of the sources are unassociated. Care was taken to characterize the sensitivity of the results to the model of interstellar diffuse gamma-ray emission used to model the bright foreground, with the result that 161 sources at low Galactic latitudes and toward bright local interstellar clouds are flagged as having properties that are strongly dependent on the model or as potentially being due to incorrectly modeled structure in the Galactic diffuse emission.