This paper deals with virtualised Network Function Placement and chaining over cloud and NFV environments. We propose a polynomial-time algorithm for joint VNF chain placement that is based on a recursive optimization approach. The key idea is to benefit from the robustness of the recursion paradigm that was used to solve many optimization problems. We demonstrate the potential of our solution by comparing it to previous work. We conduct performance evaluation first through extensive simulations and then using a real cloud testbed. The obtained results show that our proposed algorithm achieves better performance in terms of resource usage, execution time, acceptance rate and revenue of the cloud provider