We present constraints on the nature of the first galaxies selected at 350 μm. The sample includes galaxies discovered in the deepest blank-field survey at 350 μm (in the Boötes Deep Field) and also later serendipitous detections in the Lockman Hole. In determining multiwavelength identifications, the 350 μm position and map resolution of the second generation Submillimeter High Angular Resolution Camera are critical, especially in the cases where multiple radio sources exist and the 24 μm counterparts are unresolved. Spectral energy distribution templates are fitted to identified counterparts, and the sample is found to comprise IR-luminous galaxies at 1 < z < 3 predominantly powered by star formation. The first spectrum of a 350 μm selected galaxy provides an additional confirmation, showing prominent dust grain features typically associated with star-forming galaxies. Compared to submillimeter galaxies selected at 850 and 1100 μm, galaxies selected at 350 μm have a similar range of far-infrared color temperatures. However, no 350 μm selected sources are reliably detected at 850 or 1100 μm. Galaxies in our sample with redshifts 1 < z < 2 show a tight correlation between the far- and mid-infrared flux densities, but galaxies at higher redshifts show a large dispersion in their mid- to far-infrared colors. This implies a limit to which the mid-IR emission traces the far-IR emission in star-forming galaxies. The 350 μm flux densities (15 < S 350 < 40 mJy) place these objects near the Herschel/SPIRE 350 μm confusion threshold, with the lower limit on the star formation rate density suggesting the bulk of the 350 μm contribution will come from less luminous infrared sources and normal galaxies. Therefore, the nature of the dominant source of the 350 μm background—star-forming galaxies in the epoch of peak star formation in the universe—could be more effectively probed using ground-based instruments with their angular resolution and sensitivity offering significant advantages over space-based imaging.