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We present chemical abundances derived from high-resolution Magellan/Magellan Inamori Kyocera Echelle spectra of the nine brightest known red giant members of the ultra-faint dwarf galaxy Reticulum II (Ret II). These stars span the full metallicity range of Ret II (−3.5 < [Fe/H] < −2). Seven of the nine stars have extremely high levels of r-process material ([Eu/Fe] ~ 1.7), in contrast to the extremely low neutron-capture element abundances found in every other ultra-faint dwarf galaxy studied to date. The other two stars are the most metal-poor stars in the system ([Fe/H] < −3), and they have neutron-capture element abundance limits similar to those in other ultra-faint dwarf galaxies. We confirm that the relative abundances of Sr, Y, and Zr in these stars are similar to those found in r-process halo stars, but they are ~0.5 dex lower than the solar r-process pattern. If the universal r-process pattern extends to those elements, the stars in Ret II display the least contaminated known r-process pattern. The abundances of lighter elements up to the iron peak are otherwise similar to abundances of stars in the halo and in other ultra-faint dwarf galaxies. However, the scatter in abundance ratios is large enough to suggest that inhomogeneous metal mixing is required to explain the chemical evolution of this galaxy. The presence of low amounts of neutron-capture elements in other ultra-faint dwarf galaxies may imply the existence of additional r-process sites besides the source of r-process elements in Ret II. Galaxies like Ret II may be the original birth sites of r-process enhanced stars now found in the halo.