We propose a new and innovative gas-turbine system using fuel-rich hydrogen combustion, which we call a chemical gas-turbine system. It involves a fuel-rich hydrogen-air combustor as a major component. We have focused on a coaxial diffusion flame under normal pressure. The effects of equivalence ratio and swirl number have been investigated by measuring temperature profiles, gas compositions, and flame structures using direct observations of OH radical emissions. The flames were shortened and NOx emission decreased with swirling under fuel-rich conditions.