  New observations indicate that ultrafaint dwarf galaxies (UFD) -- the least
luminous systems bound by dark matter halos (<10^5 Lsun) -- may have formed
before reionization. The extrapolated virial masses today are uncertain with
estimates ranging from 10^8 Msun to 10^9 Msun. We show that the progenitor halo
masses of UFDs can be as low as Mvir = 10^7 Msun. Under the right conditions,
such a halo can survive the energy input of a supernova and its radiative
progenitor. A clumpy medium is much less susceptible to both internal and
external injections of energy. It is less prone to SN sweeping because the
coupling efficiency of the explosive energy is much lower than for a diffuse
ISM. With the aid of the 3D hydro/ionization code Fyris, we show that
sufficient baryons are retained to form stars following a single supernova
event in dark matter halos down to Mvir ~ 10^7 Msun with radiative cooling. The
gas survives the SN explosion, is enriched with the abundance yields of the
discrete events, and reaches surface densities where low mass stars can form.
Our highest resolution simulations reveal why cooling is so effective in
retaining gas compared to any other factor. In the early stages, the super-hot
metal-enriched SN ejecta exhibit strong cooling, leading to much of the
explosive energy being lost. Consistent with earlier work, the baryons do *not*
survive in smooth or adiabatic models in the event of a supernova. The smallest
galaxies carry signatures of the earliest epochs of star formation, which may
distinguish a small primordial galaxy from one that was stripped down to its
present size through tidal interaction. We discuss these results in the context
of local UFDs and damped Ly-alpha systems (z~2) at very low metallicity ([Fe/H]
~ -3). We show that both classes of objects are consistent with primordial
low-mass systems that have experienced only a few enrichment events.
