Carbon, nitrogen, and hydrogen are elements ubiquitous on Earth and the Universe; essential and present in most systems, whether biological, industrial, or planetary. Despite their fundamental importance, their high-pressure ternary phase diagram is largely unknown. This proposal aims to extend the exploration of hydrogen carbonitride compounds by subjecting simple precursor molecules to ultra-high pressures up to 180 GPa and temperatures above 2000 K. The primary goal is to synthesize and characterize new thermodynamically stable ternary C–N–H phases, building on our previous work that identified the structure of two novel C(NH)2 compounds at pressures up to 45 GPa. These will achieved using single-crystal X-ray diffraction in laser-heated diamond anvil cells. The outcomes of this investigation will be compared to first-principle calculations and will serve as a much-needed benchmark. Moreover, they could also lead to the discovery of binary C–N, C–H, and N–H materials.