The early chemical evolution of the Galaxy and the Universe is
vital to our understanding of a host of astrophysical phenomena.
Since the most metal-poor Galactic stars are relics from the
high-redshift Universe, they probe the chemical and dynamical
conditions as the Milky Way began to form, the origin and evolution of
the elements, and the physics of nucleosynthesis.  They also provide
constraints on the nature of the first stars, their associated
supernovae and initial mass function, and early star and galaxy
formation.  I will discuss examples of the most metal-poor Galactic
stars with extreme and unusual abundance patterns that can help
elucidate the supernovae responsible for their chemical signatures.
Furthermore, stars displaying a strong overabundance of the heaviest
elements, in particular uranium and thorium, can be radioactively
dated, giving formation times ~13 Gyr ago, similar to the ~13.7 Gyr
age of the Universe. I then transition to a description of recent
discoveries of extremely metal-poor stars in dwarf satellites of the
Milky Way.  Their stellar chemical signatures support the concept that
small systems analogous to the surviving dwarf galaxies were the
building blocks of the Milky Way's low-metallicity halo.  This opens a
new window for studying galaxy formation through stellar chemistry.