The millimeter transient sky is largely unexplored, with measurements limited to follow-up of objects detected at other wavelengths. High-angular-resolution telescopes, designed for measurement of the cosmic microwave background (CMB), offer the possibility to discover new, unknown transient sources in this band-particularly the afterglows of unobserved gamma-ray bursts (GRBs). Here, we use the 10 m millimeter-wave South Pole Telescope, designed for the primary purpose of observing the CMB at arcminute and larger angular scales, to conduct a search for such objects. During the 2012-2013 season, the telescope was used to continuously observe a 100 deg 2 patch of sky centered at R.A. 23 h 30 m and decl. −55°using the polarization-sensitive SPTpol camera in two bands centered at 95 and 150 GHz. These 6000 hr of observations provided continuous monitoring for day-to month-scale millimeter-wave transient sources at the 10 mJy level. One candidate object was observed with properties broadly consistent with a GRB afterglow, but at a statistical significance too low (p = 0.01) to confirm detection.