We propose an indexing technique and an index selection algorithm for optimal OLAP query processing in object database systems, Although there are many research results on the relational database systems for OLAP Query processing, few researches have been done on the object database systems. Since OLAP queries represent complex business logic on a huge data ware-house, object database systems supporting the OLAP queries should have higher performance. Proposed bitmap index structure is an extension of conventional bitmap indexes for adapting object databases and provides higher performance with lower space overhead. We also propose a linear time solution of the index selection problem that will be used in the OLAP query optimization process.