The ternary rhodium hydride Li3RhH6 was synthesized by the reaction of lithium hydride with rhodium under a hydrogen pressure of 80 bar. X-ray investigations on powdered samples and an elastic neutron diffraction experiment on the deuterated compound led to the complete structure determination (space group: Pnma, Z = 4). The atomic arrangement is isotypic to the Na3RhH6 structure type. The crystal structure contains isolated [RhH6](3-) octahedra, which are separated by the lithium ions.