We present a novel approach for self-assembled growth of GaN quantum wires (QWRs) exhibiting strong confinement in two spatial dimensions. The GaN QWRs are formed by selective nucleation on {1120} (a-plane) facets formed at the six intersections of {1100} (m-plane) sidewalls of AlN/GaN nanowires used as a template. Based on microscopy observations we have developed a 3D model explaining the growth mechanism of QWRs. We show that the QWR formation is governed by self-limited pseudomorphic growth on the side facets of the nanowires (NWs). Quantum confinement in the QWRs is confirmed by the observation of narrow photoluminescence lines originating from individual QWRs with emission energies up to 4.4 eV. Time-resolved photoluminescence studies reveal a short decay time (∼120 ps) of the QWR emission. Capping of the QWRs with AlN allows enhancement of the photoluminescence, which is blue-shifted due to compressive strain. The emission energies from single QWRs are modelled assuming a triangular cross-section resulting from self-limited growth on a-plane facets. Comparison with the experimental results yields an average QWR diameter of about 2.7 nm in agreement with structural characterization. The presented results open a new route towards controlled realization of one-dimensional semiconductor quantum structures with a high potential both for fundamental studies and for applications in electronics and in UV light generation.