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 P63/m (Nr 176), with the lattice parameters a = 8.0270(2) Å and c = 5.6240(1) Å, Z=2. The structure comprises [CrN3] 5trigonal planar units, and [HBa6] 11+ octahedral units. The presence of anionic hydrogen in the structure has been verified by 1 H NMR experiments. DFT calculations show that the addition of hydrogen increases the stability of the phase versus Ba3CrN3. The two d-electrons of Cr 4+ are located in the non-bonding dz 2 orbital, rendering Ba3CrN3H non-magnetic and insulating.