The first definite discoveries of extragalactic deuterium are reported. DCO^+ has been detected in three and DCN has been measured in one star-forming region of the Large Magellanic Cloud (LMC). While the HCO^+/DCO^+ abundance ratios are found to be 19 \pm 3, 24 \pm 4 and 67 \pm 18 for N113, N44BC and N159HW, respectively, a HCN/DCN abundance ratio of 23 \pm 5 is obtained for N113. These results are consistent with a gas temperature of about 20\,K and a D/H ratio of about 1.5 \times 10^{-5}, consistent with that observed in the Galaxy. If the cloud temperature is closer to 30\,K, then a D/H ratio is required to be up to an order of magnitude larger. Because this ratio provides a lower limit to the primordial D/H ratio, it indicates that the baryon mass density alone is unable to close the universe
