The South Pole Telescope (SPT) has surveyed hundreds of square degrees to milli-Jansky levels at 1.4 mm and 2.0 mm. We report here on sources of point-like emission detected in the 1.4 and 2.0 mm bands in an 87 deg ² field, centered at R.A. 5^h30^m, decl. -55°, and observed in 2008. Based on the ratio of flux in these two bands, we are able to separate the detected sources into two populations, one consistent with synchrotron emission from active galactic nuclei (AGN) and one consistent with thermal emission from dust. We present source counts for each population from 11 to 640 mJy at 1.4 mm and from 4.4 to 800 mJy at 2.0 mm. We detect 119 synchrotron-dominated sources and 49 dust-dominated sources at S/N > 4.5 in at least one band. All of the most significantly detected members of the synchrotron-dominated population are associated with sources in previously published radio catalogs and/or in our own long-wavelength follow-up observations. Some of the dust-dominated sources are associated with nearby (z << 1) galaxies whose dust emission is also detected by the Infrared Astronomy Satellite (IRAS). However, most of the bright, dust-dominated sources have no counterparts in any existing catalog. We argue that these sources represent the rarest, brightest, and possibly strongly-lensed members of the population commonly referred to as sub-millimeter galaxies (SMGs). Because these sources are selected at longer wavelengths than in typical SMG surveys, they are expected to have a higher mean redshift distribution than objects currently in the literature, and may provide a new window on galaxy formation in the early universe.