  We utilize metal-poor stars in the local, ultra-faint dwarf galaxies (UFDs;
L_tot < 10^5 L_sun) to empirically constrain the formation process of the first
galaxies. Since UFDs have much simpler star formation histories than the halo
of the Milky Way, their stellar populations should preserve the fossil record
of the first supernova (SN) explosions in their long-lived, low-mass stars.
Guided by recent hydrodynamical simulations of first galaxy formation, we
develop a set of stellar abundance signatures that characterize the
nucleosynthetic history of such an early system if it was observed in the
present-day universe. Specifically, we argue that the first galaxies are the
product of chemical "one-shot" events, where only one (long-lived) stellar
generation forms after the first, Population III, SN explosions. Our abundance
criteria thus constrain the strength of negative feedback effects inside the
first galaxies. We compare the stellar content of UFDs with these one-shot
criteria. Several systems (Ursa Major II, and also Coma Berenices, Bootes I,
Leo IV, Segue 1) largely fulfill the requirements, indicating that their
high-redshift predecessors did experience strong feedback effects that shut off
star formation. We term the study of the entire stellar population of a dwarf
galaxy for the purpose of inferring details about the nature and origin of the
first galaxies "dwarf galaxy archaeology". This will provide clues to the
connection of the first galaxies, the surviving, metal-poor dwarf galaxies, and
the building blocks of the Milky Way.
