  We present the discovery of a very faint stellar system, SMASH 1, that is
potentially a satellite of the Large Magellanic Cloud. Found within the Survey
of the MAgellanic Stellar History (SMASH), SMASH 1 is a compact ($r_h =
9.1^{+5.9}_{-3.4}$ pc) and very low luminosity (M_V = -1.0 +/- 0.9,
$L_V=10^{2.3 +/- 0.4}$ Lsun) stellar system that is revealed by its sparsely
populated main sequence and a handful of red-giant-branch candidate member
stars. The photometric properties of these stars are compatible with a
metal-poor ([Fe/H]=-2.2) and old (13 Gyr) isochrone located at a distance
modulus of ~18.8, i.e. a distance of ~57 kpc. Situated at 11.3$^\circ$ from the
LMC in projection, its 3-dimensional distance from the Cloud is ~13 kpc,
consistent with a connection to the LMC, whose tidal radius is at least 16 kpc.
Although the nature of SMASH 1 remains uncertain, its compactness favors it
being a stellar cluster and hence dark-matter free. If this is the case, its
dynamical tidal radius is only <19 pc at this distance from the LMC, and
smaller than the system's extent on the sky. Its low luminosity and apparent
high ellipticity ($\epsilon=0.62^{+0.17}_{-0.21}$) with its major axis pointing
toward the LMC may well be the tell-tale sign of its imminent tidal demise.
