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Self-stabilizing the quantum key distribution (QKD) system is essential to evaluate eavesdroppers’ information accurately. We develop and verify a polarization-insensitive time-bin decoder chip for QKD with the hybrid asymmetric Faraday-Michelson interferometer (AFMI) based on the planar lightwave circuit (PLC). Compared with existing chip-based QKD works, the scheme can intrinsically compensate for the polarization perturbation to quantum signals and thus work at arbitrary temperatures. We experimentally verify the chips in a time-bin QKD system at the clocking rate of 1.25 GHz and obtain an average secure key rate (SKR) of 1.34 Mbps over a 50 km fiber channel with an optimized analysis model. The steady variations of the quantum bit error and SKR with random polarization disturbance demonstrate that PLC-based AFMIs are available for developing self-stable QKD systems.