We describe CST, an online algorithm for constructing skill trees from demonstration trajectories. CST segments a demonstration trajectory into a chain of component skills, where each skill has a goal and is assigned a suitable abstraction from an abstraction library. These properties permit skills to be improved eciently using a policy learning algorithm. Chains from multiple demonstration trajectories are merged into a skill tree. We show that CST can be used to acquire skills from human demonstration in a dynamic continuous domain, and from both expert demonstration and learned control sequences on the uBot-5 mobile manipulator.