Network services have been significantly increased in today's enterprise networks. The time and cost of deploying these services are recently considered as critical challenges for enterprise networks. Network Functions Virtualization (NFV) is a promising solution to offer cost-efficient, scalable and more rapid deployment of such services. It allows the implementation of fine-grained services as a chain of Virtual Network Functions (VNFs). These chains need to be placed in the network. The chain placement is critical since it effects on both quality of service (QoS) and the provider cost. This paper formulates the problem of VNF placement and chaining as an Integer Linear Program (ILP) and proposes a Cost-efficient Centrality-based VNF Placement and chaining algorithm (CCVP). The objective is to find the optimal number of VNFs along with their locations in such a manner that the provider cost is minimized. Apart from cost minimization, the support for large-scale environments with a large number of servers and end-users is an important feature of the proposed algorithm. Finaly, the algorithm behavior is analyzed through simulations