The crystal structure of the lithium ion conductor α-Li_3.00Ga_0.33SiO₄ has been determined from Rietveld refinement of time-of-flight high-resolution powder neutron diffraction data. It is orthorhombic, with space group C222₁, and has an oxygen arrangement that is a distortion of primitive tetragonal packing. Si, Ga and Li atoms occupy tetrahedral and octahedral sites within this oxygen framework. Li and Ga sites are fractionally occupied but certain pairs of face-sharing sites have combined occupancies of unity. The relationship between this structure and those of rutile, Li₄SiO₄, Li_3.4Ga_0.2SiO₄, Li₅GaSi₂O₈ and γ-LiAlO₂ is discussed. The nature of the Li₄SiO₄(s.s.)–α(s.s.) phase transition is also discussed.