This paper is concerned with the problem of computing views of OWL ontologies using a forgetting-based approach. In traditional relational databases, a view is a subset of a database, whereas in ontologies, a view is more than a subset; it contains not only axioms contained in the original ontology, but also newly derived axioms entailed by the original ontology (implicitly contained in the original ontology). Specifically, given an ontology O, the signature sig(O) of O is the set of all terms in O, and a view V of O is a new ontology obtained from O using only part of O’s signature, namely the target signature, while preserving all logical entailments up to the target signature. Computing views of ontologies is useful for applications such as ontology-based query answering, in the sense that the view can be used as a substitute of the original ontology to answer queries formulated with the target signature, and also useful for security purposes, in the sense that it restricts users from viewing certain information of an ontology. Forgetting is a form of non-standard reasoning concerned with eliminating from an ontology a subset of its signature, namely the forgetting signature, in such a way that all logical entailments are preserved up to the target signature. Forgetting can thus be used as an ontology engineering tool to compute views of ontologies – the solution of forgetting a set F of terms from an ontology O is the view V of O for the target signature sig(O)F. In this paper, we introduce a forgetting-based method for computing views of OWL ontologies specified in the description logic ALCHOI, the basic ALC extended with role hierarchy, nominals and inverse roles. The method is terminating and sound. Despite the method not being complete, an evaluation with a prototype implementation of the method on a corpus of real-world ontologies has shown superb results. This is very useful from the perspective of the Semantic Web, as it provides knowledge engineers with a powerful approach/tool for creating views of OWL ontologies.