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Multiferroic materials host both ferroelectricity and magnetism, offering potential for magnetic memory and spin transistor applications. Here, we report a multiferroic chalcogenide semiconductor Cu_1−xMn_1+ySiTe₃(0.04 ≤x≤ 0.26; 0.03 ≤y≤ 0.15), which crystallizes in a polar monoclinic structure (Pmspace group). It exhibits a canted antiferromagnetic state below 35 kelvin, with magnetic hysteresis and remanent magnetization under 15 kelvin. We demonstrate multiferroicity and strong magnetoelectric coupling through magnetodielectric and magnetocurrent measurements. At 10 kelvin, the magnetically induced electric polarization reaches ~0.8 microcoulombs per square centimeter, comparable to the highest value in oxide multiferroics. We also observe possible room-temperature ferroelectricity. Given that multiferroicity is very rare among transition metal chalcogenides, our finding sets up a unique materials platform for designing multiferroic chalcogenides.