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 re-keying 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, 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.