One of the main research directions along which the future Internet is evolving can be identified in the paradigmatic shift from a network of hosts toward a network of caches. Yet, several questions remain concerning the scalability of individual algorithms (e.g., name based lookup and routing) and components (e.g., caches) of these novel Information Centric Networking (ICN) architectures. Exploiting a peculiar characteristics of ICN (i.e., the fact that contents are split in chunks), and the nature of video streaming (which dominates Internet traffic), this paper proposes a novel two-layers caching scheme that allows multi-Terabyte caches to sustain content streaming at multi-Gbps speed. We model the system as an extension, to the case of chunked contents, of the well known Che approximation, that has the advantage of being very simple and accurate at the same time. Simulations under synthetic and realistic trace-driven traffic confirm the accuracy of the analysis and the feasibility of the proposed architecture.