Network Function Virtualization (NFV) is a promising technology that promises to significantly reduce the operational costs of network services by deploying virtualized network functions (VNFs) to commodity servers in place of dedicated hardware middleboxes. The VNFs are typically running on virtual machine instances in a cloud infrastructure, where the virtualization technology enables dynamic provisioning of VNF instances, to process the fluctuating traffic that needs to go through the network functions in a network service. In this paper, we target dynamic provisioning of enterprise network services-expressed as one or multiple service chains-in cloud datacenters, and design efficient online algorithms without requiring any information on future traffic rates. The key is to decide the number of instances of each VNF type to provision at each time, taking into consideration the server resource capacities and traffic rates between adjacent VNFs in a service chain. In the case of a single service chain, we discover an elegant structure of the problem and design an efficient randomized algorithm achieving a e/(e-1) competitive ratio. For multiple concurrent service chains, an online heuristic algorithm is proposed, which is O(1)-competitive. We demonstrate the effectiveness of our algorithms using solid theoretical analysis and trace-driven simulations.