We report the discovery of a cool metal-poor, main-sequence star exhibiting large excesses of r-process elements. This star is one of two newly discovered cool subdwarfs (effective temperatures of 5000 K) with extremely low metallicity ([Fe/H]<-3) identified from follow-up high-resolution spectroscopy of metal-poor candidates from the Sloan Digital Sky Survey. SDSS J2357-0052 has [Fe/H]=-3.4 and [Eu/Fe]=+1.9, and exhibits a scaled solar r-process abundance pattern of heavy neutron-capture elements. This is the first example of an extremely metal-poor, main-sequence star showing large excesses of r-process elements; all previous examples of the large r-process-enhancement phenomena have been associated with metal-poor giants. The metallicity of this object is the lowest, and the excess of Eu ([Eu/Fe]) is the highest, among the r-process-enhanced stars found so far. We consider possible scenarios to account for the detection of such a star, and discuss techniques to enable searches for similar stars in the future. Comment: 16 pages, 3 figures, 2 tables, ApJL in press