La Cilla is the eighteenth-century tithe house, the building where the Catholic Church collected its share of the island's harvest — wheat, barley, lentils — from Lanzarote farmers throughout the colonial period. The squat single-storey building, on the corner of the plaza, has thick walls and a heavy iron-bound door, designed to keep both grain and tax collectors safe.
Today La Cilla is used as a small interpretation centre with displays on Teguise's history. It is more often shut than open, but worth circling on a walk around the centre even from the outside; the dark stonework around the doorway is one of the better surviving examples of the volcanic masonry that defines the village.