The heteroepitaxy of III-V semiconductors on silicon is a promising approach for making silicon a photonic platform. Mismatches in material properties, however, present a major challenge, leading to high defect densities in the epitaxial layers and adversely affecting radiative recombination processes. However, nanostructures, such as quantum dots, have been found to grow defect-free even in a suboptimal environment. Here we present the first realization of indium phosphide quantum dots on exactly oriented Si(001), grown by metal-organic vapour-phase epitaxy. We report electrically driven single-photon emission in the red spectral region, meeting the wavelength range of silicon avalanche photodiodes' highest detection efficiency.