Accurate photometric redshifts are calculated for nearly 200,000 galaxies to a 4.5 km flux limit of 613 kJy in the 8.5 deg super(2) Spitzer IRAC Shallow Survey. Using a hybrid photometric redshift algorithm incorporating both neural net and template-fitting techniques, calibrated with over 15,000 spectroscopic redshifts, a redshift accuracy of s= 0.06(1 + z) is achieved for 95% of galaxies at 0 < z < 1.5. The accuracy is s= 0.12(1 + z) for 95% of active galactic nuclei (AGNs) at 0 < z < 3. Redshift probability functions, central to several ongoing studies of the galaxy population, are computed for the full sample. We demonstrate that these functions accurately represent the true redshift probability density, allowing the calculation of valid confidence intervals for all objects. These probability functions have already been used to successfully identify a population of Spitzer-selected high-redshift (z > 1) galaxy clusters. We present one such spectroscopically confirmed cluster at (z) = 1.24, ISCS J1434.5+3427. Finally, we present a measurement of the 4.5 km-selected galaxy redshift distribution.