Quantum key distribution (QKD) promises security stemming from the laws of quantum physics. QKD devices based on integrated chips not only provides miniaturization, but also enhanced performance, which is important to practical and scalable networks. Here we report the realization of a relay server for measurement-device-independent QKD based on a heterogeneous superconducting-silicon-photonic chip. Silicon waveguides and beam splitters are used for optical guidance and interference. Waveguide integrated superconducting nanowire single-photon detectors are used to detector single photons. We show Hong-Ou-Mandel interference between weak coherent states with a visibility of 48%(2%). Our system generates 733 sifted bits at about 71 dB attenuation (equivalent to 358 km standard fiber) with a quantum bit error rate of 3.5%(0.7%). The fabrication processes of our device are compatible with standard thin-film technology. Together with integrated QKD transmitters, a scalable, chip-based and cost-effective QKD network can be realized in the near future.