The reaction of carbon and CaH2 in a calcium/lithium flux mixture produces crystals of the new compound Ca2LiC3H. This phase forms with a new structure type in tetragonal space group P4/mbm (a = 6.8236(1) angstrom, c = 3.7518(1) angstrom, Z = 2, R-1 = 0.0151). This is a stuffed variant of the Cs-2(NH2)N-3 structure, containing hydride anions in octahedral sites; the structure determination by single-crystal X-ray diffraction surprisingly allowed the hydrogen to be detected. The Ca2LiC3H structure also features the rarely seen C-3(4-) carbide anion; the protolysis reaction of this compound with ammonium chloride produces C3H4. The electronic properties of Ca2LiC3H were studied by quantum-chemical calculations including band structure and electron localization function (ELF) analysis; the phase is a charge-balanced semiconductor with a calculated band gap of 0.48 eV. This is in agreement with Li-7, C-13, and H-1 MAS NMR data, which show resonances in the ionic region instead of the Knight shifted region. ELF analysis of the theoretical nonhydrided Ca2LiC3 structure confirms the ability of these calculations to properly locate hydrides and supports the structural model based on X-ray diffraction data.