Estique is a district of Tarata, a province of the department of Tacna, Peru. Its capital is Estique.
Following the 1883 Treaty of Ancón, Chile established a province to administer its newly acquired territory south of the Sama River. Due to differing interpretations of the rivercourse, the area's administration by Chile proved controversial. Tarata was made a sub-delegation of Tacna, with its jurisdiction including the former Peruvian districts of Tarata, Tarucachi and Estique. The sub-delegation was elevated to department from 1911 to 1921, after which it was disestablished and handed over to Peru in 1925.