Modular high-temperature gas-cooled reactors (MHTGRs) offer a high degree of passive safety. The low power density of the reactor and the high heat capacity of the graphite core result in slow transients that do not challenge the integrity of the robust TRISO fuel. Another benefit of this fuel form and the surrounding graphite is their superior ability to retain fission products under all anticipated normal and off-normal conditions, which limits reactor accident source terms to very low values. In this paper, we develop estimates of the source term for a generic MHTGR to illustrate the performance of the radionuclide barriers that comprise the MHTGR functional containment. We also examine the influence of initial fuel quality, fuel performance/failure, reactor outlet temperature, and retention outside of the reactor core on the resultant source term to the environment.