Summary: Consider a hierarchical network in which each node periodically issues a request for an object drawn from a fixed set of unit-size objects. Suppose further that the following conditions are satisfied: the frequency with which each node accesses each object is known; each node has a cache of known capacity; any cache can be accessed by any node; and any request is satisfied by the closest node with a copy of the desired object, at a cost proportional to the distance between the accessing node and the closest copy. In such an environment, it is desirable to fill the available cache space with copies of objects in such a way that the average access cost is minimized. We provide both exact and approximate polynomial-time algorithms for this hierarchical placement problem. Our exact algorithm is based on a reduction to min-cost flow, and does not appear to be practical for large problem sizes. Thus we are motivated to search for a faster approximation algorithm. Our main result is a simple constant-factor approximation algorithm for the hierarchical placement problem that admits an efficient distributed implementation.