Quantum Key Distribution (QKD) is a prominent application in the field of quantum cryptography providing information-theoretic security for secret key exchange. The implementation of QKD systems on photonic integrated circuits (PICs) can reduce the size and cost of such systems and facilitate their deployment in practical infrastructures. To this end, continuous-variable (CV) QKD systems are particularly well-suited as they do not require single-photon detectors, whose integration is presently challenging. Here we present a CV-QKD receiver based on a silicon PIC capable of performing balanced detection. We characterize its performance in a laboratory QKD setup using a frequency multiplexed pilot scheme with specifically designed data processing allowing for high modulation and secret key rates. The obtained excess noise values are compatible with asymptotic secret key rates of 2.4 Mbit/s and 220 kbit/s at an emulated distance of 10 km and 23 km, respectively. These results demonstrate the potential of this technology towards fully integrated devices suitable for high-speed, metropolitan-distance secure communication.