Angle dispersive x-ray diffraction measurements of oxygen single crystals in a helium pressure transmitting medium have been performed up to 133 GPa at room temperature. The crystalline structure of metallic zeta oxygen, above 96 GPa, is shown to be associated with a continuous displacive structural transformation taking place in the ab plane of the monoclinic C2/m cell of the insulator epsilon phase. Although of first order, the change of crystalline structure to the metallic zeta phase from the epsilon phase is found to be isosymmetric, in agreement with recent calculations. Our Raman spectroscopy measurements on a single crystal of the zeta phase corroborate the present structure assignment. The interplay between metallization and structural changes is disclosed.