Experimental evidence is presented for a scale-free transition from an unordered to an ordered state in a 2D complex plasma that differs from the KTHNY theory of phase transitions in 2D systems. The transition is characterized by the formation and growth of ordered domains. A fractal relationship is found between the domain areas and domain boundary lengths, which can be explained by a recent theoretical model. The experimental findings are supported by a molecular dynamics simulation of a 2D particle system.