A sensitive search for the rare decays Ω- → Λπ- and Θ0 → pπ- 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 |ΔS| = 2 nonleptonic hyperon decays, provided the decays occur through parity-odd operators. We obtain the branching-fraction limits B(Ω- → Λπ-) < 2.9 × 10-6 and B(Θ0 → pπ-) < 8.2 × 10-6, both at 90% confidence level. © 2005 The American Physical Society.