The title hydride and its deuteride were successfully synthesized. The crystal structure of the deuteride was determined by time-of-flight neutron powder diffraction. BaAlD5 crystallizes with a new orthorhombic structure in space group Pna2(1) (No. 33), cell parameters a = 9.194(1) Angstrom, b = 7.0403(9) Angstrom, and c = 5.1061(6) Angstrom, Z = 4. BaAlH5 is the first example that contains one-dimensional zigzag chains of [AlH6] along the crystallographic c axis.