Service Function Chaining (SFC) has become an integral part of every emerging application to satisfy its specific demand. Due to the massive increase in such diverse applications, there is a need for an efficient solution for flexible SFC orchestration. In this context, deploying SFC across domains can be a promising way to provide the required network services through cost-effective resource utilization. However, the operation of Multi-Domain SFC (MD-SFC) mainly has a trade-off between privacy and performance. While sharing the detailed network information, such as topology and resource availability, is important for the efficient MD-SFC orchestration, the network operators are not willing to disclose such private and detailed network information about the domain network. As a result, there is always a higher demand for privacy preservation while employing efficient MD-SFC orchestration. In this paper, we present pSMART, a lightweight, privacy-aware service function chain orchestration in a multi-domain NFV/SDN scenario. The main purpose of pSMART is to utilize less sensitive information, to reduce privacy and security risks, and to employ learning based decision making for efficient MD-SFC mapping. We quantify and analyse the gain of the proposed pSMART approach in terms of privacy-preservation and response time. The simulation results show that the proposed pSMART approach achieves a higher level of privacy and optimizes the response time of MD-SFC orchestration. © 2020 Elsevier B.V.