We present spectra of six metal-poor stars in two of the ultra-faint dwarf galaxies orbiting the Milky Way (MW), Ursa Major II, and Coma Berenices obtained with the Keck/High Resolution Echelle Spectrometer (HIRES). These observations include the first high-resolution spectroscopic observations of extremely metal-poor ([Fe/H]<-3.0) stars not belonging to the MW halo field star population. We obtain abundance measurements and upper limits for 26 elements between carbon and europium. The entire sample of stars spans a range of -3.2<[Fe/H]<-2.3, and we confirm that each galaxy contains a large intrinsic spread of Fe abundances. A comparison with MW halo stars of similar metallicities reveals substantial agreement between the abundance patterns of the ultra-faint dwarf galaxies and the MW halo for the light, {alpha}, and iron-peak elements (C to Zn). The abundances of neutron-capture elements (Sr to Eu) in the ultra-faint dwarf galaxies are extremely low, consistent with the most metal-poor halo stars, but not with the typical halo abundance pattern at [Fe/H]>~-3.0. Not only are our results broadly consistent with a galaxy formation model that predicts that massive dwarf galaxies are the source of the metal-rich component ([Fe/H]>-2.5) of the MW halo, but they also suggest that the faintest known dwarfs may be the primary contributors to the metal-poor end of the MW halo metallicity distribution.