Proxy caches have become a central mechanism for reducing the latency of web document retrieval. While caching alone reduces latency for previously requested documents, web document prefetching could mask latency for previously unseen, but correctly predicted requests. We describe a prefetching algorithm suitable for use in a network of hierarchical web caches; this algorithm observes requests to a cache and its ancestors, and initiates prefetching for predicted future requests if prefetching is likely to reduce the overall latency seen by the cache's clients. We introduce a novel cost-benefit model that allows us to judge the value of any cached or prefetched document, which we use to state a formal prefetching policy. Extensive simulations were run to judge the improvements offered by prefetching, and our approach is quantitatively compared to the method currently in use.