Oxygen is in many ways a unique element: It is the only known diatomic molecular magnet, and it exhibits an unusual O(8) cluster in its high-pressure solid phase. Pressure-induced molecular dissociation as one of the fundamental problems in physical sciences has been reported from theoretical or experimental studies of diatomic solids H(2), N(2), F(2), Cl(2), Br(2), and I(2) but remains elusive for molecular oxygen. We report here the prediction of the dissociation of molecular oxygen into a polymeric spiral chain O(4) structure (space group I4(1)/acd, θ-O(4)) above 1.92-TPa pressure using the particle-swarm search method. The θ-O(4) phase has a similar structure as the high-pressure phase III of sulfur. The molecular bonding in the insulating ε-O(8) phase or the isostructural superconducting ζ-O(8) phase remains remarkably stable over a large pressure range of 0.008-1.92 TPa. The pressure-induced softening of a transverse acoustic phonon mode at the zone boundary V point of O(8) phase might be the ultimate driving force for the formation of θ-O(4). Stabilization of θ-O(4) turns oxygen from a superconductor into an insulator by opening a wide band gap (approximately 5.9 eV) that originates from the sp(3)-like hybridized orbitals of oxygen and the localization of valence electrons.