Title: It's the little things: ultra-faint satellites of isolated dwarf galaxies Abstract: In the currently favored cosmological paradigm, all galaxies are embedded within dark matter halos that are themselves filled with smaller dark matter clumps in a hierarchical manner. Observationally verifying the existence of these small clumps is one of the most important goals in modern cosmology. We expect that the smallest should be largely free of stars because the ambient ionizing background prevents them from accreting much gas. But below what mass do we expect all subhalos to be completely dark? We run ultra-high resolution zoom-in simulations of isolated dwarf galaxies with GIZMO (Hopkins 2014), a state-of-the-art code that utilizes the highly sophisticated FIRE (Feedback in Realistic Environments) recipes (Hopkins et al. 2014) for converting gas into stars and capturing the energy fed back from those stars into the surrounding medium. Using these simulations, we predict that ultra-faint satellite galaxies (M* ~ 3,000 Msun) should exist around isolated dwarf galaxies (M* ~ 1e6 Msun). These satellites survive the ionizing background radiation by forming their stars in the first billion years after the Big Bang. Importantly, we show that these tiny galaxies should be observable in the local universe. If they are detected, it would provide evidence that dark matter substructure is truly hierarchical, as predicted in the standard paradigm.