In network function virtualization (NFV), the placement of the virtual network function (VNF) significantly affects the load on switches and the efficiency of bandwidth utilization. Suboptimal placement of VNFs in service chains increases the flow rules in the switches and the ping-pong traffic among the VNFs. This paper presents LightChain, an efficient polynomial run time approach for optimizing VNF placement and service chaining in NFV. LightChain forms the directed acyclic graph of the given service chains and applies topological sorting to the graph. The significance of the proposed approach is as follows: 1) The minimum hop-count in each service chain, 2) Reduction of flow rules on SDN switches, and 3) Elimination of ping-pong traffic. Evaluation results show that LightChain can determine the placement locations of the VNFs in a reasonably short time. Our comparison results with other approach show that LightChain installs a lower number of flow rules in the switches. © 2016 IEEE.