  Variable emission from Sgr~A*, the luminous counterpart to the super-massive
black hole at the center of our Galaxy, arises from the innermost portions of
the accretion flow. Better characterization of the variability is important for
constraining models of the low-luminosity accretion mode powering Sgr~A*, and
could further our ability to use variable emission as a probe of the strong
gravitational potential in the vicinity of the
$4\times10^{6}\mathrm{M}_{\odot}$ black hole. We use the \textit{Herschel}
Spectral and Photometric Imaging Receiver (SPIRE) to monitor Sgr~A* at
wavelengths that are difficult or impossible to observe from the ground. We
find highly significant variations at 0.25, 0.35, and 0.5 mm, with temporal
structure that is highly correlated across these wavelengths. While the
variations correspond to $<$1% changes in the total intensity in the
\textit{Herschel} beam containing Sgr~A*, comparison to independent,
simultaneous observations at 0.85 mm strongly supports the reality of the
variations. The lowest point in the light curves, $\sim$0.5 Jy below the
time-averaged flux density, places a lower bound on the emission of Sgr~A* at
0.25 mm, the first such constraint on the THz portion of the SED. The
variability on few hour timescales in the SPIRE light curves is similar to that
seen in historical 1.3 mm data, where the longest time series is available, but
the distribution of variations in the sub-mm do not show a tail of
large-amplitude variations seen at 1.3 mm. Simultaneous X-ray photometry from
XMM-Newton shows no significant variation within our observing period, which
may explain the lack of very large variations if X-ray and submillimeter flares
are correlated.
