  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.
