Crystal growth experiments in the system BaO–Al2O3 yielded single crystals of a new Ba oxo-aluminate with composition Ba4Al2O7. The title compound is orthorhombic, with cell parameters a = 11.3126(5), b = 11.7045(9), c = 27.1850(14) Å , space group Cmca. The structure was solved by direct methods followed by difference Fourier synthesis from X-ray single crystal diffraction data (R1 = 0.048 for 1213 independent observed reflections and 135 parameters). The main building units of tetrabarium aluminate are Al3O10 trimers and isolated AlO4 tetrahedra. Seven crystallographically different Ba sites crosslink between the tetrahedral groups and are co-ordinated by six to nine oxygen ligands. The structure is closely related to the mineral kilchoanite (Ca6[SiO4][Si3O10]) and the first representative of an unbranched oligo-aluminate with triple tetrahedra.