  Many extensions of the minimal supersymmetric standard model contain
superfields for quarks which are singlets under weak isospin with electric
charge -1/3. 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 Z_3
"baryon parity" of Ibanez 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.
