Network Function Virtualization (NFV) is an emerging paradigm that turns hardware-dependent implementation of network functions (i.e., middleboxes) into software modules running on virtualized platforms, for significant cost reduction and ease of management. Such virtual network functions (VNFs) commonly constitute service chains, to provide network services that traffic flows need to go through. Efficient deployment of VNFs for network service provisioning is key to realize the NFV goals. Existing efforts on VNF placement mostly deal with offline or one-time placement, ignoring the fundamental, dynamic deployment and scaling need of VNFs to handle practical time-varying traffic volumes. This work investigates dynamic placement of VNF service chains across geo-distributed datacenters to serve flows between dispersed source and destination pairs, for operational cost minimization of the service chain provider over the entire system span. An efficient online algorithm is proposed, which consists of two main components: (1) A regularization-based approach from online learning literature to convert the offline optimal deployment problem into a sequence of one-shot regularized problems, each to be efficiently solved in one time slot; (2) An online dependent rounding scheme to derive feasible integer solutions from the optimal fractional solutions of the one-shot problems, and to guarantee a good competitive ratio of the online algorithm over the entire time span. We verify our online algorithm with solid theoretical analysis and trace-driven simulations under realistic settings.