In this work, the phase diagram of ${\mathrm{Li}}_{x}{\mathrm{CoO}}_{2}$ is calculated from first principles for x ranging from 0 to 1. Our calculations indicate that there is a tendency for Li ordering at $x=\frac{1}{2}$ in agreement with experiment [J. N. Reimers and J. R. Dahn, J. Electrochem. Soc. 139, 2091 (1992)]. At low Li concentration, we find that a staged compound is stable in which the Li ions selectively segregate to every other Li plane leaving the remaining Li planes vacant. We do not find the two-phase region observed at high Li concentration and speculate that this two-phase region is caused by the metal-insulator transition that occurs at concentrations slightly below $x=1.$