High indium incorporation in InGaN is highly desirable for realizing high performance green and red III-nitride based light-emitting diodes. However, the large lattice mismatch between InGaN and GaN results in a high compressive strain energy density in InGaN, which leads to limited indium incorporation and high threading dislocation densities. In this work, we demonstrate the growth of dislocation-free InGaN layers on the sidewalls of GaN nanowires grown via Ni-catalyzed metal organic chemical vapor deposition (MOCVD). Indium incorporations as high as 40-60% in the shell layers were reached, as confirmed by scanning transition electron microscopy (STEM), energy dispersive x-ray spectroscopy, and spatially resolved cathodoluminescence microscopy. In order to better understand the results, the strain energy density distribution in an InGaN/GaN coaxial nanowire was calculated using finite element analysis. The indium distribution in the InGaN shell layer was found to be influenced by the strain energy density distribution. The observed high indium incorporation and lack of dislocations in the InGaN shell growth is attributed to the unique strain relaxation of the InGaN/GaN coaxial nanowires. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.