We report a theoretical study on the gas-phase hydrogen-bonded complexes formed between ozone and hydroperoxyl radical, which are of interest in atmospheric chemistry. We have employed CASSCF, CASPT2, QCISD, and CCSD(T) theoretical approaches employing 6-311+G(2df,2p) and aug-cc-pVTZ basis sets, and we have found three complexes whose stabilities are computed to be 2.02, 1.19, and 1.34 kcal/mol, respectively, at 0 K. In addition, we have also found three transition states connecting these complexes that lie below the energy of the separate reactants. To help for possible experimental identification of these hydrogen-bonded complexes, we report also the computed harmonic vibrational frequencies along with the frequency shifts of the complexes, relative to the monomers, and the computed rotational constants.