Unique dynamics using inanimate molecular assemblies have drawn a great amount of attention for demonstrating prebiomimetic molecular systems. For the construction of an organized logic combining two fundamental dynamics of life, we demonstrate here a molecular system that exhibits both division and self-propelled motion using oil droplets. The key molecule of this molecular system is a novel cationic surfactant containing a five-membered acetal moiety, and the molecular system can feed the self-propelled oil droplet composed of a benzaldehyde derivative and an alkanol. The division dynamics of the self-propelled oil droplets were observed through the hydrolysis of the cationic surfactant in bulk solution. The mechanism of the current dynamics is argued to be based on the supply of "fresh" oil components in the moving oil droplets, which is induced by the Marangoni instability. We consider this molecular system to be a prototype of self-reproducing inanimate molecular assembly exhibiting self-propelled motion.