Transactional Memory is a concurrent programming API in which concurrent threads synchronize via transactions (instead of locks). Although this model has mostly been studied in the context of multiprocessors, it has attractive features for distributed systems as well. In this paper, we consider the problem of implementing transactional memory in a network of nodes where communication costs form a metric. The heart of our design is a new cache-coherence protocol, called the Ballistic protocol, for tracking and moving up-to-date copies of cached objects. For constant-doubling metrics, a broad class encompassing both Euclidean spaces and growth-restricted networks, this protocol has stretch logarithmic in the diameter of the network.