Barium-cobaltate-based perovskite (BaCoO3-δ) and barium-cobaltate-based nanocomposites have been intensively studied in energy storage and conversion devices mainly due to flexible oxygen stoichiometry and tunable nonprecious transition metal oxidation states. Although a rich and complex family of structural polymorphs has already been reported for these perovskites in the literature, the potential structural evolution that may occur during the oxygen reduction reaction and the oxygen evolution reaction has not been investigated so far. In this study, we synthesized and characterized the lowest Co-oxidation state possible in the compound, BaCoO2, which exhibits a quartz-derived, trigonal structure with a helicoidally corner-sharing, CoO4-tetrahedral-framework as already proposed by Spitsbergen et al. Oxygen can reversibly be inserted in such a crystal structure to form BaCoO3-δ, i.e., with 0 ≤ δ ≤ 1, based on the results of an in situ coupled thermogravimetric - neutron diffraction study and which presents therefore giant oxygen capacity storage due to the extreme tunability of the electronic configuration of the cobalt cations which defines the fundamental origins of the materials performance. The reversible conversion of BaCoO2 to BaCoO3-δ associated with a similar electronic conductivity above 900 K permits to clarify the high potential of BaCoO3-δ-based energy storage and conversion devices.