Accurate photometric redshifts are calculated for nearly 200,000 galaxies to a 4.5 micron flux limit of \sim 13 \mu Jy in the 8.5 deg ^ { 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 \sigma = 0.06 ( 1 + z ) is achieved for 95 % of galaxies at 0 < z < 1.5 . The accuracy is \sigma = 0.12 ( 1 + z ) for 95 % of AGN 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 \left < z \right > = 1.24 , ISCS J1434.5+3427 . Finally , we present a measurement of the 4.5 \mu m–selected galaxy redshift distribution .