Service Function Chaining (SFC) has been proposed as an enhanced Software-Defined Networking/Network Function Virtualization (SDN/NFV) technology to accommodate the network service requirements of various applications. In particular, the provisioning of network service functions, such as in-network caching, transcoding, and multicasting, improves the Quality of Experience (QoE) of video streaming services and reduces the traffic load. However, these functionalities require high computational resources of the network nodes, and over-provisioning the computational resources causes another problem. In this paper, we propose an elastic Function Offloading Network (FON) for SFC. FON adopts a highly scalable functional call using Information-Centric Networking (ICN) technology and provides valuable functions for common SFC networks. We experimented with FON implementation running on a real SFC network and evaluated the throughput, traffic load, and QoE of the streaming applications. The results show that FON significantly outperforms an existing SFC framework, which does not have any offloading functionality.