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Quantum networks are likely to have a profound impact on the way we compute and communicate in the future. In order to wire together superconducting quantum processors over kilometer-scale distances, we need transducers that can generate entanglement between the microwave and optical domains with high fidelity. We present an integrated electro-optic transducer that combines low-loss lithium niobate photonics with superconducting microwave resonators on a sapphire substrate. Our triply resonant device operates in a dilution refrigerator and converts microwave photons to optical photons with an on-chip efficiency of 6.6×10^−6 and a conversion bandwidth of 20 MHz. We discuss design trade-offs in this device, including strategies to manage acoustic loss, and outline ways to increase the conversion efficiency in the future.