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New insight into the superconducting properties of HgBa2CuO4 (Hg-1201) cuprates is provided by combined measurements of electrical resistivity and single crystal X-ray diffraction under pressure. The changes induced by increasing pressure up to 20 GPa in optimally doped single crystals were investigated. The resistivity measurements as a function of temperature show a metallic behavior up to ~10 GPa that gradually passes into an insulating state, typical of charge ordering, which totally suppresses superconductivity above 13 GPa. The changes in resistivity are accompanied by the apparition of sharp Bragg peaks in the X-ray diffraction patterns, indicating that the charge ordering is accompanied by a 3D oxygen ordering. Considering that pressure induces a charge transfer of about 0.02 at 10 GPa, our results are the first observation of charge order competing with superconductivity developed in the overdoped region of the phase diagram of a Hg-based cuprate.