The chlorine tetroxide radical and its anion have been investigated with unrestricted Hartree-Fock, density functional and hybrid Hartree-Fock/density functional methods, perturbation theory, and coupled cluster methods. It is predicted that the minimum on the ClO4 radical potential energy surface corresponds to the B-2(2) ground electronic state, a C-2v-symmetry structure. The C-3v structure identified experimentally lies a few kcal mol(-1) higher energetically. A C-s symmetry structure lies very close energetically to the C-2v minimum at some levels of theory. Adiabatic electron affinities, equilibrium geometries, harmonic vibrational frequencies, infrared intensities, isotopic shifts, and dipole moments are presented for all methods. Comparisons with recent experimental vibrational data for the radical are made. It is predicted that the C-2v equilibrium geometry of the ground state is R(e(Cl-O1))=1.502 Angstrom, R(e(Cl-O2))=1.424 Angstrom, theta(e1)=93.6 degrees and theta(e2)=114.2 degrees. The adiabatic electron affinity of the ClO4 radical is predicted to lie near 5.2 eV.