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}-3.4+5.9 {pc}) and very low luminosity ({M}V=-1.0+/- 0.9, {L}V={10}2.3+/- 0.4 {L}ȯ ) 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 from the LMC in projection, its three-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 (ε ={0.62}-0.21+0.17) with its major axis pointing toward the LMC may well be the tell-tale sign of its imminent tidal demise.