The hydride Ba3Si4Hx (x = 1-2) was prepared by sintering the Zintl phase Ba3Si4, which contains Si-4(6-) butterfly-shaped polyanions, in a hydrogen atmosphere at pressures of 10-20 bar and temperatures of around 300 degrees C. Initial structural analysis using powder neutron and X-ray diffraction data suggested that Ba3Si4Hx adopts the Ba3Ge4C2 type [space group I4/mcm (No. 140), a approximate to 8.44 angstrom, c approximate to 11.95 angstrom, 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 Ba3Si4H is not charge-balanced. First-principles computations revealed an alternative structural scenario for Ba3Si4Hx, which is based on filling pyramidal Ba-5 interstices in Ba3Si4. The limiting composition is x = 2 [space group P4(2)/mmm (No. 136), a approximate to 8.4066 angstrom, c approximate to 12.9186 angstrom, Z = 8], and for x > 1, Si atoms also adopt tetrahedron-shaped polyanions. Transmission electron microscopy investigations showed that Ba3Si4Hx is heavily disordered in the c direction. Most plausible is to assume that Ba3Si4Hx has a variable H content (x = 1-2) and corresponds to a random intergrowth of P- and I-type structure blocks. In either form, Ba3Si4Hx is classified as an interstitial hydride. Polyanionic hydrides in which H is covalently attached to Si remain elusive.