An accurate calculation of bound and resonance spectra of the non-rotating odd O-2 exchange symmetry HO2 radical is presented. The calculation has been carried out by a recently developed iterative technique which uses filter diagonalization of a sparse matrix of the system Hamiltonian with absorbing boundary conditions, We were able to obtain 361 bound states and some 232 isolatable resonances (Gamma<0.01 eV) in a wide energy range corresponding to the HO2-->H+O-2 unimolecular decomposition reaction. It is shown that all resonances found have the same nature as the bound states in that they ail are localized in the same region of space over the deep potential well, and moreover the extrapolated smoothed density of the bound states merges easily with the smoothed density of the resonance states. The level statistics for both bound and resonance states indicates a highly chaotic regime consistent with the random matrix theory. Strong mode mixing makes assignments of most bound and resonance states impossible because the corresponding wave functions do not show any simple pattern. Interestingly, the randomly fluctuating high resolution density of states after smoothing shows a structure resembling two basic frequencies corresponding to the O-2 stretch and HOO bend motion of the HO2 molecule.