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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  bit/s 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.