We present a new method to synthesize bulk indium nitride by means of a simple solid-state chemical reaction carried out under hydrostatic high-pressure/high-temperature conditions in a multi-anvil apparatus, not involving gases or solvents during the process. The reaction occurs between the binary oxide In2O3 and the highly reactive Li3N as the nitrogen source, in the powder form. The formation of the hexagonal phase of InN, occurring at 350 °C and P ≥ 3 GPa, was successfully confirmed by powder X-ray diffraction, with the presence of Li2O as a unique byproduct. A simple washing process in weak acidic solution followed by centrifugation allowed us to obtain pure InN polycrystalline powders as a precipitate. With an analogous procedure, it was possible to obtain pure bulk GaN, from Ga2O3 and Li3N at T ≥ 600 °C and P ≥ 2.5 GPa. These results point out, particularly for InN, a clean, and innovative way to produce significant quantities of one of the most promising nitrides in the field of electronics and energy technologies.