Measurement-device-independent quantum key distribution (MDI-QKD) removes all detector side channels and enables secure QKD with an untrusted relay. It is suitable for building a star-type quantum access network, where the complicated and expensive measurement devices are placed in the central untrusted relay and each user requires only a low-cost transmitter, such as an integrated photonic chip. Here, we experimentally demonstrate a 1.25 GHz silicon photonic chip-based MDI-QKD system using polarization encoding. The photonic chip transmitters integrate the necessary encoding components for a standard QKD source. We implement random modulations of polarization states and decoy intensities, and demonstrate a finite-key secret rate of 31 bps over 36 dB channel loss (or 180 km standard fiber). This key rate is higher than state-of-the-art MDI-QKD experiments. The results show that silicon photonic chip-based MDI-QKD, benefiting from miniaturization, low-cost manufacture and compatibility with CMOS microelectronics, is a promising solution for future quantum secure networks.