Numerical simulations based on the Lambda-CDM model of cosmology predict a large number of as yet unobserved Galactic dark matter satellites. We report the results of a Large Area Telescope (LAT) search for these satellites via the gamma-ray emission expected from the annihilation of weakly interacting massive particle (WIMP) dark matter. Some dark matter satellites are expected to have hard gamma-ray spectra, finite angular extents, and a lack of counterparts at other wavelengths. We sought to identify LAT sources with these characteristics, focusing on gamma-ray spectra consistent with WIMP annihilation through the $b \bar b$ channel. We found no viable dark matter satellite candidates using one year of data, and we present a framework for interpreting this result in the context of numerical simulations to constrain the velocity-averaged annihilation cross section for a conventional 100 GeV WIMP annihilating through the $b \bar b$ channel. Show Partial Abstract