We present the redshift distribution of a complete, unbiased sample of 24 μm sources down to fν(24 μ m) = 300 μ Jy (5 σ). The sample consists of 591 sources detected in the Boötes field of the NOAO Deep Wide-Field Survey. We have obtained optical spectroscopic redshifts for 421 sources (71%). These have a redshift distribution peaking at z ~ 0.3, with a possible additional peak at z ~ 0.9, and objects detected out to z = 4.5. The spectra of the remaining 170 (29%) exhibit no strong emission lines from which to determine a redshift. We develop an algorithm to estimate the redshift distribution of these sources, based on the assumption that they have emission lines but that these lines are not observable due to the limited wavelength coverage of our spectroscopic observations. The redshift distribution derived from all 591 sources exhibits an additional peak of extremely luminous (L8–1000 μ m > 3 × 1012 L☉) objects at z ~ 2, consisting primarily of sources without observable emission lines. We use optical line diagnostics and IRAC colors to estimate that 55% of the sources within this peak are AGN-dominated. We compare our results to published models of the evolution of infrared-luminous galaxies. The models which best reproduce our observations predict a large population of star-formation-dominated ULIRGs at z > 1.5 rather than the AGN-dominated sources we observe.