  We present the redshift distribution of a complete, unbiased sample of 24
micron sources down to fnu(24 micron) = 300 uJy (5-sigma). The sample consists
of 591 sources detected in the Bootes 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 (L(8-1000 micron) > 3 x 10^{12} Lsun)
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.
