We describe a new method for unsupervised structure learning of a hierarchical compositional model (HCM) for deformable objects. The learning is unsupervised in the sense that we are given a training dataset of images containing the object in cluttered backgrounds but we do not know the position or boundary of the object. The structure learning is performed by a bottom-up and top-down process. The bottom-up process is a novel form of hierarchical clustering which recursively composes proposals for simple structures to generate proposals for more complex structures. We combine standard clustering with the suspicious coincidence principle and the competitive exclusion principle to prune the number of proposals to a practical number and avoid an exponential explosion of possible structures. The hierarchical clustering stops automatically, when it fails to generate new proposals, and outputs a proposal for the object model. The top-down process validates the proposals and fills in missing elements. We tested our approach by using it to learn a hierarchical compositional model for parsing and segmenting horses on Weizmann dataset. We show that the resulting model is comparable with (or better than) alternative methods. The versatility of our approach is demonstrated by learning models for other objects (e.g., faces, pianos, butterflies, monitors, etc.). It is worth noting that the low-levels of the object hierarchies automatically learn generic image features while the higher levels learn object specific features.