Although the local resistivity of semiconducting silicon in its standard crystalline form can be changed by many orders of magnitude by doping with elements, superconductivity has so far never been achieved. Hybrid devices combining silicon's semiconducting properties and superconductivity have therefore remained largely underdeveloped. Here we report that superconductivity can be induced when boron is locally introduced into silicon at concentrations above its equilibrium solubility. For sufficiently high boron doping (typically 100 p.p.m.) silicon becomes metallic. We find that at a higher boron concentration of several per cent, achieved by gas immersion laser doping, silicon becomes superconducting. Electrical resistivity and magnetic susceptibility measurements show that boron-doped silicon (Si:B) made in this way is a superconductor below a transition temperature T(c) approximately 0.35 K, with a critical field of about 0.4 T. Ab initio calculations, corroborated by Raman measurements, strongly suggest that doping is substitutional. The calculated electron-phonon coupling strength is found to be consistent with a conventional phonon-mediated coupling mechanism. Our findings will facilitate the fabrication of new silicon-based superconducting nanostructures and mesoscopic devices with high-quality interfaces.