Generally, a service request must specify its required virtual network functions (VNFs) and their specific order, which is known as the service function chain (SFC). When mapping SFCs, network providers face many challenges due to the requirements of maintaining the correct order and satisfying other constraints of VNFs. Furthermore, SFC orchestration becomes a more difficult problem when considered in multi-domain networks, because the confidentiality of the topology information of each domain must be considered. In this paper, we study the problem of SFC orchestration across multiple domains. We first use the full mesh aggregation approach to construct an abstracted network to guide the orchestration process, and then propose two efficient methods for SFC partitioning. Based on the SFC partitioning results, we also propose two heuristic algorithms for deploying the sub-chains in multiple domains. Moreover, when the partitioning results cannot be mapped completely, a feedback mechanism is used to repartition the SFC and improve the success ratio of orchestrating the SFC. Finally, to save bandwidth resources, we further improve our heuristic algorithms by migrating the deployment position of VNFs. The simulation results demonstrate that our proposed algorithm achieves better performance compared to existing solutions.