The hydride Ba(3)Si(4)H(x) (x = 1-2) was prepared by sintering the Zintl phase Ba(3)Si(4), which contains Si(4)(6-) butterfly-shaped polyanions, in a hydrogen atmosphere at pressures of 10-20 bar and temperatures of around 300 °C. Initial structural analysis using powder neutron and X-ray diffraction data suggested that Ba(3)Si(4)H(x) adopts the Ba(3)Ge(4)C(2) type [space group I4/mcm (No. 140), a ≈ 8.44 Å, c ≈ 11.95 Å, Z = 8] where Ba atoms form a three-dimensional array of corner-condensed octahedra, which are centered by H atoms. Tetrahedron-shaped Si(4) polyanions complete a perovskite-like arrangement. Thus, hydride formation is accompanied by oxidation of the butterfly polyanion, but the model with the composition Ba(3)Si(4)H is not charge-balanced. First-principles computations revealed an alternative structural scenario for Ba(3)Si(4)H(x), which is based on filling pyramidal Ba5 interstices in Ba(3)Si(4). The limiting composition is x = 2 [space group P4(2)/mmm (No. 136), a ≈ 8.4066 Å, c ≈ 12.9186 Å, Z = 8], and for x > 1, Si atoms also adopt tetrahedron-shaped polyanions. Transmission electron microscopy investigations showed that Ba(3)Si(4)H(x) is heavily disordered in the c direction. Most plausible is to assume that Ba(3)Si(4)H(x) has a variable H content (x = 1-2) and corresponds to a random intergrowth of P- and I-type structure blocks. In either form, Ba(3)Si(4)H(x) is classified as an interstitial hydride. Polyanionic hydrides in which H is covalently attached to Si remain elusive.