It is now possible to use a quantum-mechanical electronic structure theory of solids and derive, completely from "first-principles,＇＇ the voltage of a battery based on intercalation reaction energetics. Using such techniques, we investigate the structural stability, intercalation energies, and battery voltages of the two observed ordered phases ("layered" and cubic) of LiCoO2. We perform calculations for not only fully lithiated LiCO2, but also fully delithiated square CoO2 and partially delithiated Li0.5CoO2. Our calculations demonstrate that removal of Li from the cubic phase results in movement of the Li atoms from their original octahedral sites-to tetrahedral sites, forming a low-energy LiCo2O4 spine structure. The energetics of the spinel phase are shown to account for the observed marked differences in battery voltages between the cubic and layered phases of LiCoO2. A small energy barrier exists for Li motion between octahedral and tetrahedral sites, thus indicating the metastability of the high-energy octahedral sites. Finally, we point out a possible pressure-induced layered --> cubic transition in LiCoO2.