The relatively unexplored fast radio transient parameter space is known to be home to a variety of interesting sources, including pulsars, pulsar giant pulses and non-thermal emission from planetary magnetospheres. In addition, a variety of hypothesized but as-yet-unobserved phenomena, such as primordial black hole evaporation and prompt emission associated with coalescing massive objects have been suggested. The 2007 announcement by Lorimer et al. of the detection of a bright (30 Jy) radio pulse that was inferred to be of extragalactic origin and the subsequent consternation have demonstrated both the potential utility of bright radio pulses as probes of the interstellar medium and intergalactic medium, as well as the need for wide-field surveys characterizing the fast-transient parameter space. Here we present results from the 450 hour, 150 deg^2 Fly's Eye survey for bright dispersed radio pulses at the Allen Telescope Array (ATA). The Fly's Eye spectrometer produces 128 channel power spectra over a 209 MHz bandwidth, centered at 1430 MHz, on 44 independent signals paths originating with 30 independent ATA antennas. Data were dedispersed between 0 and 2000 pc cm^-3 and searched for pulses with dispersion measures greater than 50 pc cm^-3 between 625 us and 5 s in duration. No pulses were detected in the survey, implying a limiting rate of less than 2 sky^-1 hour^-1 for 10 millisecond duration pulses having apparent energy densities greater than 440 kJy us, or mean flux densities greater than 44 Jy. Here we present details of the instrument, experiment and observations, including a discussion of our results in light of other single pulse searches.