Self-movement in an oil/water system generated by chemically driven Marangoni instability was studied. Repetitive changes in the interfacial tension were monitored for a two-phase system, in which the oil phase was a nitrobenzene solution of iodine and potassium iodide and the aqueous phase contained cationic surfactant. Our findings show that inversion of the contact angle induced by a sudden increase in tension is essential for inducing marked acceleration in the self-motion of the oil droplet. The self-motion continues for 30-60 min and then terminates. The movement starts again with the addition of iodine to the oil droplet after an induction period necessary for "digestion" of the nutrient, i.e., the iodine.