The Large and Small Magellanic Clouds are unique local laboratories for studying the formation and evolution of small galaxies in exquisite detail. The Survey of the MAgellanic Stellar History (SMASH) is an NOAO community Dark Energy Camera (DECam) survey of the Clouds mapping 480 deg2 (distributed over ~2400 square degrees at ~20% filling factor) to ~24th mag in ugriz. The primary goals of SMASH are to identify low surface brightness stellar populations associated with the stellar halos and tidal debris of the Clouds, and to derive spatially resolved star formation histories. Here, we present a summary of the survey, its data reduction, and a description of the first public Data Release (DR1). The SMASH DECam data have been reduced with a ...