We present Atacama Large Millimeter/submillimeter Array (ALMA) 860 micrometer imaging of four high-redshift (z=2.8-5.7) dusty sources that were detected using the South Pole Telescope (SPT) at 1.4 mm and are not seen in existing radio to far-infrared catalogs. At 1.5 arcsec resolution, the ALMA data reveal multiple images of each submillimeter source, separated by 1-3 arcsec, consistent with strong lensing by intervening galaxies visible in near-IR imaging of these sources. We describe a gravitational lens modeling procedure that operates on the measured visibilities and incorporates self-calibration-like antenna phase corrections as part of the model optimization, which we use to interpret the source structure. Lens models indicate that SPT0346-52, located at z=5.7, is one of the most luminous and intensely star-forming sources in the universe with a lensing corrected FIR luminosity of 3.7 X 10^13 L_sun and star formation surface density of 4200 M_sun yr^-1 kpc^-2. We find magnification factors of 5 to 22, with lens Einstein radii of 1.1-2.0 arcsec and Einstein enclosed masses of 1.6-7.2x10^11 M_sun. These observations confirm the lensing origin of these objects, allow us to measure the their intrinsic sizes and luminosities, and demonstrate the important role that ALMA will play in the interpretation of lensed submillimeter sources.
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