The crystal structure of the superconductor HgBa2Ca2Cu3O8+δ has been determined by neutron powder diffraction techniques at room temperature and at 10 K. The compound crystallizes with the symmetry of space group P4/mmm and lattice parameters a=3.8501(1), c=15.7837(9) A ̊. The structure is described by the sequence of layers: ...[(CuO2)(Ca)(CuO2)(BaO)(HgOδ(BaO)(CuO2)(Ca)]... The compound, prepared by a solid-state reaction between HgO and the precursor Ba2Ca2Cu3Ox at a pressure of 18 kbar and 880°C, has an oxygen composition corresponding to δ=0.41 (2). This extra oxygen is located on the layer of the mercury atoms at the sites 1 2, 1 2, 1 2. The superconducting transition temperature for the as-prepared sample is Tc=133 K. No evidence has been found of orthorhombic distortions, nor for substitution of some of the Hg atoms by Cu. The copper and oxygen atoms of the layers (CuO2) are coplanar for the Z=0 (CuO2 plane and almost perfectly coplanar for the others. No phase transition occurs down to 10 K.