Current Grid deployments for LHC computing (namely the WLCG infrastructure) do not allow efficient parallel interactive processing of data. In order to allow physicists to interactively access subsets of data (e.g. for algorithm tuning and debugging before running over a full dataset) parallel analysis facilities based on PROOF have been deployed by the ALICE experiment at CERN and elsewhere. Whereas large Tier-1 centres may afford to build such facilities at the expense of their Grid farms, or exploit the large number of jobs finishing at any given time to quickly collect a number of nodes to temporarily allocate for interactive work, this is likely not to be true for smaller Tier-2 centres. Leveraging on the virtualization of highly performant multi-core machines it is possible to build a fully virtual analysis facility on the same Worker Nodes that compose an existing LCG Grid Farm. Using the Xen paravirtualization hypervisor, it is then possible to dynamically move resources from the batch instance to the interactive one when needed, minimizing latencies and wasted resources. We present the status of the prototype being developed, and some experience from the very first users.