This paper considers the optimal placement of Baseband Unit (BBU) function split in Cloud Radio Access Networks (C-RANs) which is an essential key technology in C-RAN deployment. In particular, the BBU function split is modeled as directed chains to be mapped to a network infrastructure. As such, we propose an Integer Linear Program (ILP) formulation for small and medium size networks. Alternatively, we introduce four heuristic algorithms with significantly less complexity. We then benchmark the four heuristic algorithms based on the construction of a multi-stage graph. The simulation results strongly confirm the efficiency and scalability of our algorithms as well as their ability to achieve an optimal solution.