Density functional theory is used to explore the possibility of inducing impurity band ferromagnetism in monolayers of semiconducting MoS2 by introducing holes into the narrow Mo 4d band that forms the top of the valence band. A large out-of-plane anisotropy is found for unpaired spins bound to the substitutional acceptor impurities V, Nb, and Ta that couple ferromagnetically for all but the shortest separations. Using the separation-dependent exchange interactions as the input to Monte Carlo calculations, we estimate ordering temperatures as a function of the impurity concentration. For about 9% of V impurities, Curie temperatures in excess of 160 K are predicted. The singlet formation at short separations that limits the ordering temperature is explained and we suggest how it can be circumvented.