We present a new algorithm for reasoning in the description logic SHIQ, which is the most prominent fragment of the Web Ontology Language OWL. The algorithm is based on ordered binary decision diagrams (OBDDs) as a datastructure for storing and operating on large model representations. We thus draw on the success and the proven scalability of OBDDbased systems. To the best of our knowledge, we present the very first agorithm for using OBDDs for reasoning with general Tboxes.