Manipulating an articulated object requires perceiving its kinematic hierarchy: its parts, how each can move, and how those motions are coupled. Previous work has explored perception for kinematics, but none infers a complete kinematic hierarchy on never-before-seen object instances, without relying on a schema or template. We present a novel perception system that achieves this goal. Our system infers the moving parts of an object and the kinematic couplings that relate them. To infer parts, it uses a point cloud instance segmentation neural network and to infer kinematic hierarchies, it uses a graph neural network to predict the existence, direction, and type of edges (i.e. joints) that relate the inferred parts. We train these networks using simulated scans of synthetic 3D models. We evaluate our system on simulated scans of 3D objects, and we demonstrate a proof-of-concept use of our system to drive real-world robotic manipulation.