In the vicinity of x ~ 0.75, LixCoO2 has potential as a thermoelectric, since it has a high Seebeck coefficient and metallic conductivity. We have performed the first successful single-crystal neutron diffraction study of LixCoO2 for x ~ 0.75 and have determined its superstructure. This proposal is to determine the Li ordering for x ~ 0.67, 0.87 and 0.95. There is evidence of charge ordering for x ~ 0.67, and we believe that this is due to a honeycomb lattice of Li ions. The Seebeck coefficient is a maximum in the non-metallic phase at x ~ 0.87, and there is a peak as a function of temperature that is attributed to vacancy disorder. A first order Mott transition is predicted in the semiconducting phase at x ~ 0.95, connected with the Li vacancies. The aim is to correlate the extraordinarily rich transport properties of LixCoO2 at high x with the ordering of the Li ions.