We present an AAOmega spectroscopic study of red giants in the ultra-faint dwarf galaxy Boötes I (MV ∼ -6) and the Segue 1 system (MV ∼ -1.5), either an extremely low luminosity dwarf galaxy or an unusually extended globular cluster. Both Boötes I and Segue 1 have significant abundance dispersions in iron and carbon. Boötes I has a mean abundance of [Fe/H] = -2.55 ±0.11 with an [Fe/H] dispersion of σ = 0.37 ± 0.08, and abundance spreads of Δ[Fe/H] = 1.7and Δ [C/H] = 1.5. Segue 1 has a mean of [Fe/H] = -2.7 ±0.4 with [Fe/H] dispersion of s = 0.7±0.3, and abundances spreads of Δ [Fe/H] = 1.6 and Δ[C/H] = 1.2. Moreover, Segue 1 has a radial-velocity member at four half-light radii that is extremely metal-poor and carbon-rich, with [Fe/H] = -3.5, and [C/Fe] = +2.3. Modulo an unlikely non-member contamination, the [Fe/H] abundance dispersion confirms Segue 1 as the least-luminous ultra-faint dwarf galaxy known. For [Fe/H] < -3.0, stars in the Milky Way's dwarf galaxy satellites exhibit a dependence of [C/Fe] on [Fe/H] similar to that in Galactic field halo stars. Thus, chemical evolution proceeded similarly in the formation sites of the Galaxy's extremely metal-poor halo stars and in the ultra-faint dwarf galaxies. We confirm the correlation between (decreasing) luminosity and both (decreasing) mean metallicity and (increasing) abundance dispersion in the Milky Way dwarf galaxies at least as faint as MV = - 5. The very low mean iron abundances and the high carbon and iron abundance dispersions in Segue 1 and Boötes I are consistent with highly inhomogeneous chemical evolution starting in near zero-abundance gas. These ultra-faint dwarf galaxies are apparently surviving examples of the very first bound systems.