The ultra-faint dwarf (UFD) galaxy Reticulum 2 (Ret 2) was recently discovered in images obtained by the Dark Energy Survey (Diehl et al. 2014SPIE.9149E..0VD). We have observed the four brightest red giants in Ret 2 at high spectral resolution using the Michigan/Magellan Fiber System. We present detailed abundances for as many as 20 elements per star, including 12 elements heavier than the Fe group. We confirm previous detection of high levels of r-process material in Ret 2 (mean [Eu/Fe]=+1.69+/-0.05) found in three of these stars (mean [Fe/H]=-2.88+/-0.10). The abundances closely match the r-process pattern found in the well-studied metal-poor halo star CS 22892-052. Such r-process-enhanced stars have not been found in any other UFD galaxy, though their existence has been predicted by at least one model. The fourth star in Ret 2 ([Fe/H]=-3.42+/-0.20) contains only trace amounts of Sr ([Sr/Fe]=-1.73+/-0.43) and no detectable heavier elements. One r-process enhanced star is also enhanced in C (natal [C/Fe]~+1.1). This is only the third such star known, which suggests that the nucleosynthesis sites leading to C and r-process enhancements are decoupled. The r-process-deficient star is enhanced in Mg ([Mg/Fe]=+0.81+/-0.14), and the other three stars show normal levels of {alpha}-enhancement (mean [Mg/Fe]=+0.34+/-0.03). The abundances of other {alpha} and Fe-group elements closely resemble those in UFD galaxies and metal-poor halo stars, suggesting that the nucleosynthesis that led to the large r-process enhancements either produced no light elements or produced light-element abundance signatures indistinguishable from normal supernovae.