We report the abundance analysis of new high signal-to-noise ratio (S/N) spectra of the most metal-poor ([Fe/H]=-2.95) star currently known to be a member of a dwarf galaxy, the Draco dSph red giant D119. No absorption lines for elements heavier than Ni are detected in two Keck HIRES spectra covering the 3850-6655{AA} wavelength range, a phenomenon not previously noted in any other metal-poor star. We present upper limits for several heavy-element abundances. The most stringent limits, based on the nondetection of SrII and BaII lines, indicate that the total s- and r-process enrichment of D119 is at least 100times smaller than Galactic stars of similar metallicity. The light-element abundances are consistent with the star having formed out of material enriched primarily by massive Type II supernovae (M>20-25M_{Sun}_). If this is the case, we are forced to conclude that massive, metal-poor Type II supernovae did not contribute to the r-process in the proto-Draco environment. We compare the abundance pattern observed in D119 to current predictions of prompt enrichment and pair-instability supernovae and find that the model predictions fail by an order of magnitude or more for many elements.