This paper describes a wide-coverage statistical parser that uses Combinatory Categorial Grammar (CCG) to derive dependency structures. The parser differs from most existing wide-coverage treebank parsers in capturing the long-range dependencies inherent in constructions such as coordination, extraction, raising and control, as well as the standard local predicate-argument dependencies. A set of dependency structures used for training and testing the parser is obtained from a treebank of CCG normal-form derivations, which have been derived (semi-) automatically from the Penn Treebank. The parser correctly recovers over 80% of labelled dependencies, and around 90% of unlabelled dependencies.