n-type doping in Si by shallow impurities, such as P, As, and Sb, exhibits an intrinsic limit due to the Fermi-level pinning via defect complexes at high doping concentrations. Here, we demonstrate that doping Si with the deep chalcogen donor Te by nonequilibrium processing can exceed this limit and yield higher electron concentrations. In contrast to shallow impurities, the interstitial Te fraction decreases with increasing doping concentration and substitutional Te dimers become the dominant configuration as effective donors, leading to a nonsaturating carrier concentration as well as to an insulator-to-metal transition. First-principles calculations reveal that the Te dimers possess the lowest formation energy and donate two electrons per dimer to the conduction band. These results provide an alternative insight into the physics of deep impurities and lead to a possible solution for the ultrahigh electron concentration needed in today's Si-based nanoelectronics.