A novel ternary hydride in the Mg–Cu–H system has been identified by a new synthesis method based on the direct reaction of simple hydrides under high-pressure and moderate-temperature conditions. A well-crystallized sample was obtained in a piston-cylinder hydrostatic press at moderate pressures of 3.5 GPa and temperatures around 850 °C starting from mixtures of MgH2 and Cu enclosed in platinum capsules. X-ray and neutron powder diffraction analysis were used to identify the purity of the samples and provide an accurate description of the crystal structure features. The crystal structure of Mg3CuHx was determined by ab-initio procedures from neutron powder diffraction (NPD) data in the cubic space group F-43m (No. 216), with lattice parameter a = 6.285 Å. The hydrogen positions were determined by Fourier synthesis revealing the introduction of hydrogen atoms in the system. A final Rietveld refinement of the structure gives up a Mg3CuH0.6 composition, which is consistent with the Fourier synthesis. Thermogravimetric analysis (TGA) has been carried out to determine the hydrogen desorption temperature, and to confirm the hydrogen contents. A destabilization with respect to MgH2 hydride, with a reduction of the desorption temperature of approximately 240 °C, suggests that Cu-doping of MgH2 may find applications in the hydrogen storage field.