Network services can be delivered through a service function chain (SFC) for reliability-sensitive applications. Traditional SFC protection can be employed by providing a node-link-disjoint backup path to avoid SFC disruption. However, such a backup path may not exist in the network with limited resources. In this work, we propose a chain segment protection, which can effectively protect an SFC using several backup chain segments when a node-link-disjoint backup path is not available. We investigate how to jointly embed and provide chain segment protection while reducing the backup bandwidth resources. We define this problem as SFC failure with chain segment protection (SFCF-CSP), which is proved to be NP-hard. To address SFCF-CSP, we propose an efficient heuristic algorithms called backup chain-segment embedding and protection (BCEP). The simulation results show that the proposed algorithm outperforms the approaches that are directly extended from the existing work.