In this paper, we describe a novel approach to scalable group re-keying for secure multicast. Our approach, which we call Kronos, is based upon the idea of periodic group re-keying. We first motivate our approach by showing that if a group is re-keyed on each membership change, as the size of the group increases and/or the rate at which members leave and join the group increases, the frequency of rekeying becomes the primary bottleneck for scalable group re-keying. In contrast, Kronos can scale to handle large and dynamic groups because the frequency of re-keying is independent of the size and membership dynamics of the group. Next, we describe how Kronos can be used in conjunction with distributed key management frameworks such as IGKMP [10], that use a single group-wide session key for encrypting communications between members of the group. Using a detailed simulation, we compare the performance tradeoffs between Kronos and other key management protocols.