Recent analysis of strongly-lensed sources in the Hubble Frontier Fields indicates that the rest-frame UV luminosity function of galaxies at $z=$6--8 rises as a power law down to $M_mathrm{UV}=-15$, and possibly as faint as -12.5. We use predictions from a cosmological radiation hydrodynamic simulation to map these luminosities onto physical space, constraining the minimum dark matter halo mass and stellar mass that the Frontier Fields probe. While previously-published theoretical studies have suggested or assumed that early star formation was suppressed in halos less massive than $10^9$--$10^{11} M_odot$, we find that recent observations demand vigorous star formation in halos at least as massive as (3.1, 5.6, 10.5)$times10^9 M_odot$ at $z=(6,7,8)$. Likewise, we find that Frontier Fields observations probe down to stellar masses of (8.1, 18, 32)$times10^6 M_odot$; that is, they are observing the likely progenitors of analogues to Local Group dwarfs such as Pegasus and M32. Our simulations yield somewhat different constraints than two complementary models that have been invoked in similar analyses, emphasizing the need for further observational constraints on the galaxy-halo connection.
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