The first group of anionic noble-gas hydrides with the general formula HNgBeO- (Ng = Ar, Kr, Xe, Rn) is predicted through MP2, Coupled-Cluster, and Density Functional Theory computations employing correlation-consistent atomic basis sets. We derive that these species are stable with respect to the loss of H, H-, BeO, and BeO-, but unstable with respect to Ng + HBeO-. The energy barriers of the latter process are, however, high enough to suggest the conceivable existence of the heaviest HNgBeO- species as metastable in nature. Their stability arises from the interaction of the H- moiety with the positively-charged Ng atoms, particularly with the σ-hole ensuing from their ligation to BeO. This actually promotes relatively tight Ng-H bonds featuring a partially-covalent character, whose degree progressively increases when going from HArBeO- to HRnBeO-. The HNgBeO- compounds are also briefly compared with other noble-gas anions observed in the gas phase or isolated in crystal lattices.