Prounipotent groups, over the complex numbers, are inverse limits of unipotent algebraic groups. They are the analogue for characteristic zero of pro-p groups and have many analogous properties. As with pro-p groups, free prounipotent groups exist and have a homological characterization. Unipotent groups arise in differential Galois theory from iterated anti-derivative extensions. We shall show that the closure of this produces free prounipotent groups.