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Nominal InN monolayers grown by molecular beam epitaxy on GaN(0001) are investigated combining in situ reflection high-energy electron diffraction (RHEED), transmission electron microscopy (TEM), and density functional theory (DFT). TEM reveals a chemical intraplane ordering never observed before. Employing DFT, we identify a novel surface stabilization mechanism elastically frustrated rehybridization, which is responsible for the observed chemical ordering. The mechanism also sets an incorporation barrier for indium concentrations above 25% and thus fundamentally limits the indium content in coherently strained layers.