Recent experimental studies on graphene on hexagonal boron nitride (hBN) have demonstrated that hBN is not only a passive substrate that ensures superb electronic properties of graphene's carriers, but that it actively modifies their massless Dirac fermion character through a periodic moiré potential. Here we present a theory of the plasmon excitation spectrum of massless Dirac fermions in a moiré superlattice. We demonstrate that graphene-hBN stacks offer a rich platform for plasmonics in which control of plasmon modes can occur not only via electrostatic gating but also by adjusting, e.g., the relative crystallographic alignment.