We demonstrate stable, single-frequency output from single, as-fabricated GaN nanowire lasers operating far above lasing threshold. Each laser is a linear, double-facet GaN nanowire functioning as gain medium and optical resonator, fabricated by a top-down technique that exploits a tunable dry etch plus anisotropic wet etch for precise control of the nanowire dimensions and high material gain. A single-mode linewidth of ~0.12 nm and >18 dB side-mode suppression ratio are measured. Numerical simulations indicate that single-mode lasing arises from strong mode competition and narrow gain bandwidth.