We present post-cryogenic Spitzer imaging at 3.6 and 4.5 micron with the Infrared Array Camera (IRAC) of the Spitzer/HETDEX Exploratory Large-Area (SHELA) survey. SHELA covers $sim$deg$^2$ of the Sloan Digital Sky Survey Stripe 82 region, and falls within the footprints of the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) and the Dark Energy Survey. The HETDEX blind R $sim$ 800 spectroscopy will produce $sim$ 200,000 redshifts from the Lyman-$alpha$ emission for galaxies in the range 1.9 < z < 3.5, and an additional $sim$200,000 redshifts from the [OII] emission for galaxies at z < 0.5. When combined with deep ugriz images from the Dark Energy Camera, K-band images from NEWFIRM, and other ancillary data, the IRAC photometry from Spitzer will enable a broad range of scientific studies of the relationship between structure formation, galaxy stellar mass, halo mass, AGN, and environment over a co-moving volume of $sim$0.5 Gpc$^3$ at 1.9 < z < 3.5. Here, we discuss the properties of the SHELA IRAC dataset, including the data acquisition, reduction, validation, and source catalogs. Our tests show the images and catalogs are 80% (50%) complete to limiting magnitudes of 22.0 (22.6) AB mag in the detection image, which is constructed from the weighted sum of the IRAC 3.6 and 4.5 micron images. The catalogs reach limiting sensitivities of 1.1 $mu$Jy at both 3.6 and 4.5 micron (1$sigma$, for R=2 arcsec circular apertures). As a demonstration of science, we present IRAC number counts, examples of highly temporally variable sources, and galaxy surface density profiles of rich galaxy clusters. In the spirit of Spitzer Exploratory programs we provide all images and catalogs as part of the publication.
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