Recent advances in the synthetic growth of nanowires have given access to crystal phases that in bulk are only observed under extreme pressure conditions. Here, we use first-principles methods based on density functional theory and many-body perturbation theory to show that a suitable mixing of hexagonal Si and hexagonal Ge yields a direct bandgap with an optically permitted transition. Comparison of the calculated radiative lifetimes with typical values of nonradiative recombination mechanisms indicates that optical emission will be the dominant recombination mechanism. These findings pave the way to the development of silicon-based optoelectronic devices, thus far hindered by the poor light emission efficiency of cubic Si