New Constraints onR-Parity-Broken Supersymmetry from Neutrinoless Double Beta Decay

New constraints on the parameters of the minimal supersymmetric standard model with explicit $R$-parity violation ( $R_p$MSSM) are obtained from the current experimental lower bound on the half-life of ${}^{76}$Ge $0\nu \beta \beta$ decay. These constraints are shown to be more stringent than those from other low-energy processes and are competitive with or even more stringent than constraints expected from accelerator searches.