The hydride NdGaH1+x (x approximate to 0.66) and its deuterized analogue were obtained by sintering the Zintl phase NdGa with the CrB structure in a hydrogen atmosphere at pressures of 10-20 bar and temperatures near 300 degrees C. The system NdGa/NdGaH1+x exhibits reversible H storage capability. H uptake and release were investigated by kinetic absorption measurements and thermal desorption mass spectroscopy, which showed a maximum H concentration corresponding to "NdGaH2" (0.93 wt % H) and a two-step desorption process, respectively. The crystal structure of NdGaH1+x was characterized by neutron diffraction (P2(1)/m, a = 4.1103(7), b = 4.1662(7), c = 6.464(1) angstrom, beta = 108.61(1)degrees Z = 2). H incorporates in NdGa by occupying two distinct positions, H1 and H2. HI is coordinated in a tetrahedral fashion by Nd atoms. The H2 position displays flexible occupancy, and H2 atoms attain a trigonal bipyramidal coordination by centering a triangle of Nd atoms and bridging two Ga atoms. The phase stability and electronic structure of NdGaH1+x, were analyzed by first-principles DFT calculations. NdGaH1H2 (NdGaH2) may be expressed as Nd3+(H1(-)[GaH2](2-). The two-dimensional polyanion [GaH](2-) features linear -H-Ga-H-Ga- chains with alternating short (1.8 A) and long (2.4 angstrom) Ga-H distances, which resembles a Peierls distortion. H2 deficiency (x < 1) results in the fragmentation of chains. For x = 0.66 arrangements with five-atom moieties, Ga-H-Ga-H-Ga are energetically most favorable. From magnetic measurements, the Curie-Weiss constant and effective magnetic moment of NdGaH1.66 were obtained. The former indicates antiferromagnetic interactions, and the latter attains a value of similar to 3.6 mu(B), which is typical for compounds containing Nd3 ions.