Many extensions of the minimal supersymmetric standard model contain superfields for quarks which are singlets under weak isospin with electric charge -13. We explore the possibility that such isosinglet quarks have low or intermediate scale masses, but do not mediate rapid proton decay because of a discrete symmetry. By imposing the discrete gauge anomaly cancellation conditions, we show that the simplest way to achieve this is to extend the Z3 “baryon parity” of Ibáñez and Ross to the isosinglet quark superfields. This can be done in three distinct ways. This strategy is not consistent with grand unification with a simple gauge group, but may find a natural place in superstring-inspired models, for example. An interesting feature of this scenario is that proton decay is absolutely forbidden.