A sensitive search for the rare decays Omega(-)--> Lambdapi(-) and Xi(0)--> ppi(-) has been performed using data from the 1997 run of the HyperCP (Fermilab E871) experiment. Limits on other such processes do not exclude the possibility of observable rates for |DeltaS| = 2 nonleptonic hyperon decays, provided the decays occur through parity-odd operators. We obtain the branching-fraction limits B(Omega(-)-->Lambdapi(-)) < 2.9 x 10(-6) and B(Xi(0)--> ppi(-)) < 8.2 x 10(-6), both at 90% confidence level.