  We consider the fate of the Wigner crystal state in a two dimensional system
of massive Dirac electrons as the effective fine structure constant $\alpha$ is
increased. In a Dirac system, larger $\alpha$ naively corresponds to stronger
electron-electron interactions, but it also implies a stronger interband
dielectric response that effectively renormalizes the electron charge. We
calculate the critical density and critical temperature associated with quantum
and thermal melting of the Wigner crystal state using two independent
approaches. We show that at $\alpha \gg 1$, the Wigner crystal state is best
understood in terms of logarithmically-interacting electrons, and that both the
critical density and the melting temperature approach a universal,
$\alpha$-independent value. We discuss our results in the context of recent
experiments in twisted bilayer graphene near the magic angle.
