Built on top of virtualization technologies, network function virtualization (NFV) provides flexible and scalable software implementation of various network functions. Virtual network functions (VNFs), which are network functions implemented as virtual machines, are chained together to provide network services. Dynamic deployment of VNFs while satisfying incoming network traffic demand is the key to cost optimization of an NFV system. Besides considering server resource capacity and incoming traffic rates, an optimal scaling policy needs to strike a balance between VNF's operational costs, the costs for maintaining VNF instances, and VNF deployment costs, additional costs when setting up new VNF instances on a server. This paper targets dynamic scaling of VNF instances in a cloud data center where multiple VNF chains are running. We propose an online scaling algorithm to adjust the deployment of VNF instances according to time-varying traffic demand, ensuring a good competitive ratio. Through theoretical analysis and trace-driven simulation, we demonstrate effectiveness of the proposed online VNF scaling algorithm.