Multi-domain networking slice orchestration is an essential technology for the programmable and cloud-native 5G network. However, existing research solutions are either based on the impractical assumption that operators will reveal all the private network information or time-consuming secure multi-party computation which is only applicable to limited computation scenarios. To provide agile and privacy-preserving end-to-end network slice orchestration services, this paper proposes NetChain, a multi-domain network slice orchestration architecture based on blockchain and trusted execution environment. Correspondingly, we design a novel consensus algorithm CoNet to ensure the strong security, scalability, and information consistency of NetChain. In addition, a bilateral evaluation mechanism based on game theory is proposed to guarantee fairness and Quality of Experience by suppressing the malicious behaviors during multi-domain network slice orchestration. Finally, the prototype of NetChain is implemented and evaluated on the Microsoft Azure Cloud with confidential computing. Experiment results show that NetChain has good performance and security under the premise of privacy-preserving.