We report the splitting of an oscillating DNA circuit into ∼700 droplets with picoliter volumes. Upon incubation at constant temperature, the droplets display sustained oscillations that can be observed for more than a day. Superimposed to the bulk behaviour, we find two intriguing new phenomena - slow desynchronization between the compartments and kinematic spatial waves - and investigate their possible origin. This approach provides a route to study the influence of small volume effects in biology, and paves the way to technological applications of compartmentalized molecular programs controlling complex dynamics.