The recently discovered stellar system Ursa Major III/UNIONS 1 (UMa3/U1) is the faintest known Milky Way satellite to date. With a stellar mass of and a half-light radius of 3 ± 1 pc, it is either the darkest galaxy ever discovered or the faintest self-gravitating star cluster known to orbit the Galaxy. Its line-of-sight velocity dispersion suggests the presence of dark matter, although current measurements are inconclusive because of the unknown contribution to the dispersion of potential binary stars. We use N-body simulations to show that, if self-gravitating, the system could not survive in the Milky Way tidal field for much longer than a single orbit (roughly 0.4 Gyr), which strongly suggests that the system is stabilized by the presence of large amounts of dark matter. If UMa3/U1 formed at the center of a ∼10$^{9}$M$_{⊙}$ cuspy LCDM halo, its velocity dispersion would be predicted to be of order ∼1 km s$^{−1}$. This is roughly consistent with the current estimate, which, neglecting binaries, places σ$_{los}$ in the range 1–4 km s$^{−1}$. Because of its dense cusp, such a halo should be able to survive the Milky Way tidal field, keeping UMa3/U1 relatively unscathed until the present time. This implies that UMa3/U1 is plausibly the faintest and densest dwarf galaxy satellite of the Milky Way, with important implications for alternative dark matter models and for the minimum halo mass threshold for luminous galaxy formation in the LCDM cosmology. Our results call for multi-epoch high-resolution spectroscopic follow-up to confirm the dark matter content of this extraordinary system.