Live virtual machine (VM) migration can move applications from one location to another without a disruption in service. However, applications often consist of multiple VMs and rely on the state of the underlying network for basic reachability, access control, and QoS functionality. Rather than migrating an individual VM, we show how to migrate an ensemble-the VMs, the network, and the management system-to a different set of physical resources. Our LIME (LIve Migration of Ensembles) design leverages recent advances in Software Defined Networking (SDN) for a clear separation between the controller and the data-plane state in the switches. Transparent to the application running on the controller, LIME clones the data-plane state to a new set of switches, and then incrementally migrates the traffic sources (e.g., the VMs). During this transition, both networks deliver traffic and LIME maintains synchronized state. Experiments with our initial prototype, built on the Floodlight OpenFlow controller, suggest that network migration does not have to be a disruptive, middle-of-the-night maintenance event, but can become an integral network management mechanism completely transparent to applications.