Time-Sensitive Networking (TSN) technology is experiencing diverse application requirements and forming a complicated standard system. It is extremely difficult to design a one-fits-all chip for all TSN applications. Therefore, application-driven TSN chip customization is inevitable. Generally, chip customization starts from a "clean-slate". For complicated ASIC chips, that results in significant development overhead. Inspired by RISC-V chips, an open-source template will significantly reduce the customization complexity. Along this road, we propose an open-source TSN chip named Fenglin-I. Fenglin-I includes a high-level abstraction to build a relationship between application requirements and chip implementation, source code of a real chip named FastTSN to provide reference code for chip implementation, and software tools to facilitate chip verification. Based on Fenglin-I, we further propose a TSN chip customization method that provides step-by-step guidance about customizing TSN chips agilely. To verify the effectiveness of Fenglin-I and the proposed customization method, we use FPGA arrays to prototype and verify FastTSN. The results show that FastTSN achieves microsecond-level transmission jitter for unicast and multicast time-critical traffic. Additionally, we demonstrate two domain-specific TSN chip customization cases in which the customized chips reuse at least 84% of FastTSN code while meeting their requirements.