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Integrated photonics has the advantages of miniaturization, low cost, and CMOS compatibility, and it provides a stable, highly integrated, and practical platform for quantum key distribution (QKD). While photonic integration of optical components has greatly reduced the overall cost of QKD systems, single-photon detectors (SPDs) have become the most expensive part of a practical QKD system. In order to circumvent this obstacle and make full use of SPDs, we have designed and fabricated a QKD receiver chip for multiple users. Our chip is based on a time-division multiplexing technique and makes use of a single set of SPDs to support up to four users' QKD. Our proof-of-principle chip-based QKD system is capable of producing an average secret key rate of 13.68 kbps for four users with a quantum bit error rate (QBER) as low as 0.51% over a simulated distance of 20 km in fiber. Our result clearly demonstrates the feasibility of multiplexing SPDs for setting QKD channels with different users using photonic integrated chip and may find applications in the commercialization of quantum communication technology.