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 systems 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.
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