We introduce a rate-based congestion control mechanism for Content-Centric Networking (CCN). It builds on the fact that one Interest retrieves at most one Data packet. Congestion can occur when aggregate conversations arrive in excess and fill up the transmission queue of a CCN router. We compute the available capacity of each CCN router in a distributed way in order to shape their conversations Interest rate and therefore, adjust dynamically their Data rate and transmission buffer occupancy. We demonstrate the convergence properties of this Hop-by-hop Interest Shaping mechanism (HoBHIS) and provide a performance analysis based on various scenarios using our ns2 simulation environment.