We study rare decays of the Omega baryon using SU(3) chiral perturbation theory, a successfuleffective field theory of quantum chromodynamics at low energies. At leading-order, we calculatethe branching fractions of the decay Ω− → Ξππ for all possible combinations of pions. For onechannel we find an order-of-magnitude discrepancy between theory and experiment. This tension isknown to exist in the non-relativistic limit, and we confirm that it remains when using a relativisticframework. Fairly independent of the values of our low energy constants we establish lower limitsfor the branching fractions, which reaffirm the gap between theory and experiment. A possibleexplanation for the gap is that the ∆I = 1/2 rule does not hold for nonleptonic Omega decays.If this were the case, fully differential distributions would be crucial to improving the theory.Here, as a baseline we present the conservative result based on the ∆I = 1/2 rule. Furthermore,at next-to-leading order we calculate the decay Ω− → Ξ0µ−νµ. We show that fully differentialdistributions will provide access to low-energy constants needed in the axial-vector transitions froma decuplet to octet baryon. The data for these rare three-body Omega decays are scarce (fullydifferential data are nonexistent), and we recommend that they be remeasured at running andupcoming experiments, such as BESIII, Belle-II, PANDA and LHCb.