Summary form only given. Multidimensional arrays have become very common in scientific and business applications. Such arrays are usually very large and hence they are stored on secondary or tertiary storage systems. For processing, various parts of a multidimensional array are typically retrieved to main memory using range queries. The performance of such queries is significantly affected by the physical organization of the target array on the storage system. Previous research has proposed an approach of this physical organization by chunking, i.e. by decomposing a multidimensional array into smaller multidimensional arrays (chunks). The parameters of the chunking process are chosen based on the storage system characteristics as well as the expected access pattern of range queries. With this approach, the average time of answering a query has been improved. The research presented in this paper extends the basic approach of chunking to a multilevel version; hence the presented approach is called multilevel chunking. We show by experiment that multilevel chunking outperforms single level chunking. The approach presented here primarily targets hard disk systems.