We report a series of experiments carried out with a dichloromethane drop deposited on the surface of an aqueous solution containing a surfactant, cetyltrimethylammonium bromide. After an induction stage during which the drop stays axisymmetric, oscillations occur along the contact line. These oscillations are succeeded by a spectacular spontaneous spinning of the drop. The latter quickly takes the form of a two-tip ‘rotor’ and the spinning rate stabilizes at a constant value, no longer varying despite the gradual changes of the drop shape and size. The drop eventually disappears due to the continual dissolution and evaporation of dichloromethane. Schlieren visualizations and particle image velocimetry are used to establish a consistent scenario capable of explaining the evolution of the system. The Marangoni effect induced by the dissolution of dichloromethane in the drop vicinity is shown to be responsible for the observed dynamics. Arguments borrowed from dynamical systems theory and from an existing low-order model allow us to explain qualitatively why the system selects the spinning configuration. The geometry of the immersed part of the drop is shown to play a crucial role in this selection process, as well as in the regulation of the spinning rate.