Motivated by the observation that electrons in graphene, in the hydrodynamic regime of transport, can be treated as a two-dimensional ultrarelativistic gas with very low shear viscosity, we examine the existence of the Rayleigh-Bénard instability in a massless electron-hole plasma. First, we perform a linear stability analysis, derive the leading contributions to the relativistic Rayleigh number, and calculate the critical value above which the instability develops.