The emerging paradigm of network function virtualization advocates deploying virtualized network functions (VNFs) on standard virtualization platforms for significant cost reduction and management flexibility. There have been system designs for managing dynamic deployment and scaling of VNF service chains within one cloud datacenter. Many real-world network services involve geo-distributed service chains, with prominent examples of mobile core networks and IP multimedia subsystems (IMSs)). Virtualizing these service chains requires efficient coordination of dynamic VNF deployment across geo-distributed data centers, calling for a new management system. This paper designs a dynamic scaling system for geo-distributed VNF service chains, using the case of an IMS. IMSs are widely used subsystems for delivering multimedia services among mobile users in a 3G/4G network, whose virtualization has been broadly advocated in the industry for reducing cost, improving network usage efficiency and enabling dynamic network topology reconfiguration for performance optimization. Our scaling system design caters to key control-plane and data-plane service chains in an IMS, combining proactive and reactive approaches for timely, cost-effective scaling of the service chains. The design principles are applicable to scaling of other systems with multiple related service chains. We evaluate our system using real-world experiments on both an emulation platform and a geo-distributed public cloud.