The phase diagram of the first layer of H2 adsorbed on top of a single graphene sheet has been calculated by means of a series of diffusion Monte Carlo simulations. We have found that, as in the case of 4He, the ground state of molecular hydrogen is a √3×√3 commensurate structure, followed, upon a pressure increase, by an incommensurate triangular solid. A striped phase of intermediate density was also considered and found lying on top of the equilibrium curve separating both commensurate and incommensurate solids.