Defects in conventional semiconductors substantially lower the photoluminescence (PL) quantum yield (QY), a key metric of optoelectronic performance that directly dictates the maximum device efficiency. Two-dimensional transition-metal dichalcogenides (TMDCs), such as monolayer MoS2, often exhibit low PL QY for as-processed samples, which has typically been attributed to a large native defect density. We show that the PL QY of as-processed MoS2 and WS2 monolayers reaches near-unity when they are made intrinsic through electrostatic doping, without any chemical passivation. Surprisingly, neutral exciton recombination is entirely radiative even in the presence of a high native defect density. This finding enables TMDC monolayers for optoelectronic device applications as the stringent requirement of low defect density is eased.