The annihilation of new dark matter candidates with masses m _ { X } in the MeV range may account for the galactic positrons that are required to explain the 511 keV \gamma -ray flux from the galactic bulge . We study the impact of MeV-mass thermal relic particles on the primordial synthesis of ^ { 2 } H , ^ { 4 } He , and ^ { 7 } Li . If the new particles are in thermal equilibrium with neutrinos during the nucleosynthesis epoch they increase the helium mass fraction for m _ { X } \lesssim 10 MeV and are thus disfavored . If they couple primarily to the electromagnetic plasma they can have the opposite effect of lowering both helium and deuterium . For m _ { X } = 4 –10 MeV they can even improve the overall agreement between the predicted and observed ^ { 2 } H and ^ { 4 } He abundances .