Description Logics (DLs) are the formal foundations of the standard web ontology languages OWL-DL and OWL-Lite. In the Semantic Web and other domains, ontologies are increasingly seen also as a mechanism to access and query data repositories. This novel context poses an original combination of challenges that has not been addressed before: (i) sufficient expressive power of the DL to capture common data modeling constructs; (ii) well established and flexible query mechanisms such as Conjunctive Queries (CQs); (iii) optimization of inference techniques with respect to data size, which typically dominates the size of ontologies. This calls for investigating data complexity of query answering in expressive DLs. While the complexity of DLs has been studied extensively, data complexity has been characterized only for answering atomic queries, and was still open for answering CQs in expressive DLs. We tackle this issue and prove a tight CONP upper bound for the problem in SHIQ, as long as no transitive roles occur in the query. We thus establish that for a whole range of DLs from AL to SHIQ, answering CQs with no transitive roles has CONP-complete data complexity. We obtain our result by a novel tableaux-based algorithm for checking query entailment, inspired by the one in , but which manages the technical challenges of simultaneous inverse roles and number restrictions (which leads to a DL lacking the finite model property).