The nitride-hydride Ba3CrN3H was obtained in single crystalline form using flux growth techniques based on alkaline earth metals. Ba3CrN3H crystallizes in the hexagonal space group P6(3)/m (Nr 176), with the lattice parameters a = 8.0270(2) angstrom, c = 5.6240(1) angstrom, and Z = 2. The structure comprises [CrN3](5-) trigonal planar units and [HBa6](11+) octahedral units. The presence of anionic hydrogen in the structure has been verified by H-1 NMR experiments. DFT calculations show that the addition of hydrogen increases the stability of the phase versus Ba3CrN3. The two d-electrons of Cr4+ are located in the nonbonding d(z)(2) orbital, rendering Ba3CrN3H nonmagnetic and insulating.