Despite many years of experimental searches for a first-order Mott transition in crystal line-doped semiconductors, none have been found. Extensive experimental work has characterized a first-order metal-insulator transition in LixCoO2, the classic material for rechargeable Li batteries, with a metallic state for x < 0.75 and insulating for x > 0.95. Using density functional theory calculations on large supercells, we identify the mechanism of this hereto anomalous metal-insulator transition as a Mott transition of impurities. Density functional theory demonstrates that for dilute Li-vacancy concentrations, the vacancy binds a hole and forms impurity states yielding a Mott insulator. The unique feature of LixCoO2 as compared with traditional doped semiconductors, such as Si:P, is the high mobility of the Li vacancies, which allows them to rearrange into two distinct phases at the temperature of the metal-insulator transition.