  We report the discovery of a unique object of uncertain nature -- but quite
possibly a disintegrating asteroid or minor planet -- orbiting one star of the
widely separated binary TIC 400799224. We initially identified the system in
data from TESS Sector 10 via an abnormally-shaped fading event in the light
curve (hereafter 'dips'). Follow-up speckle imaging determined that TIC
400799224 is actually two stars of similar brightness at 0.62" separation,
forming a likely bound binary with projected separation of ~300 au. We cannot
yet determine which star in the binary is host to the dips in flux. ASAS-SN and
Evryscope archival data show that there is a strong periodicity of the dips at
~19.77 days, leading us to believe that an occulting object is orbiting the
host star, though the duration, depth, and shape of the dips vary
substantially. Statistical analysis of the ASAS-SN data shows that the dips
only occur sporadically at a detectable threshold in approximately one out of
every three to five transits, lending credence to the possibility that the
occulter is a sporadically-emitted dust cloud. The cloud is also fairly
optically thick, blocking up to 37% or 75% of the light from the host star,
depending on the true host. Further observations may allow for greater detail
to be gleaned as to the origin and composition of the occulter, as well as to a
determination of which of the two stars comprising TIC 400799224 is the true
host star of the dips.
