Regular arrays of single atoms with stable magnetization represent the ultimate limit of ultrahigh density storage media. Here we report a self-assembled superlattice of individual and noninteracting Dy atoms on graphene grown on Ir(111), with magnetic hysteresis up to 5.6 T and spin lifetime of 1000 s at 2.5 K. The observed magnetic stability is a consequence of the intrinsic low electron and phonon densities of graphene and the 6-fold symmetry of the adsorption site. Our array of single atom magnets has a density of 115 Tbit/inch(2), defined by the periodicity of the graphene moire pattern.