  We report the results of an 87 square-degree point-source survey centered at
R.A. 5h30m, decl. -55 deg. taken with the South Pole Telescope (SPT) at 1.4 and
2.0 mm wavelengths with arc-minute resolution and milli-Jansky depth. Based on
the ratio of flux in the two bands, we 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. The 2.0 mm counts are dominated by synchrotron-dominated
sources across our reported flux range; the 1.4 mm counts are dominated by
synchroton-dominated sources above ~15 mJy and by dust-dominated sources below
that flux level. We detect 141 synchrotron-dominated sources and 47
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. 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
catalogs. We argue that these sources represent the rarest and brightest
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 and may provide a new window on galaxy formation in the early
universe.
