Lithium-ion batteries are now reaching the energy density limits set by their electrode materials, requiring new paradigms for Li+ and electron hosting in solid-state electrodes. Reversible oxygen redox in the solid state in particular has the potential to enable high energy density as it can deliver excess capacity beyond the theoretical transition-metal redox-capacity at a high voltage. Nevertheless, the structural and chemical origin of the process is not understood, preventing the rational design of better cathode materials. Here, we demonstrate how very specific local Li-excess environments around oxygen atoms necessarily lead to labile oxygen electrons that can be more easily extracted and participate in the practical capacity of cathodes. The identification of the local structural components that create oxygen redox sets a new direction for the design of high-energy-density cathode materials.