The structure of BaBiO3 at 25°C has been solved and refined with the use of neutron diffraction powder data. The valence situation is found to be BaBi3+12Bi5+12O3 rather than BaBi4+O3. The Bi3+ and Bi5+ cations take on an ordered arrangement and the resultant structure has monoclinic symmetry 12/m (a = 6.181 Å, b = 6.136 Å, c = 8.670 Å, β = 90.17°). This is the first example of an ordered perovskite in which the ordered cations are the same element, and also represents the first case of Bi3+ octahedrally coordinated to oxygen. The semiconducting properties of BaBiO3 are readily understood on the basis of the ordered structure. The structure becomes rhombohedral at about 130°C, and cubic in the region of 450°C.