Many real world applications of ontologies call for reasoning with modular ontologies. Classical approaches to reasoning with ontology assume a single centralized, consistent ontology. However, in the case of multiple, autonomously developed ontology modules, it is usually neither possible nor desirable to integrate all involved modules into a single centralized ontology. In this paper, we propose a tableau-based reasoning algorithm based on Package-based Description Logics (P-DL), an ontology language that extends description logics with language features to support modularity. The algorithm adopts a federated approach to reasoning with modular ontologies wherein each ontology module has associated with it, a local reasoner. The local reasoners communicate with each other as needed in an asynchronous fashion.