Service Function Chaining (SFC) enables dynamic steering of traffic through a set of service functions based on classification of packets, allowing network operators fine-grained and flexible control of packet flows. New paradigms like Zero Trust (ZT) pose additional requirements to the security of network architectures. This includes client authentication, confidentiality, and integrity throughout the whole network, while also being able to perform operations on the unencrypted payload of packets. However, these requirements are only partially addressed in existing SFC literature. Therefore, we first present a comprehensive analysis of the security requirements for SFC architectures. Based on this analysis, we propose a concept towards the fulfillment of the requirements while maintaining the flexibility of SFC. In addition, we provide and evaluate a proof of concept implementation, and discuss the implications of the design choices.