We report stationary, nonequilibrium potential and adsorbate patterns with an intrinsic wavelength that were observed in an electrochemical system with a specific type of current/electrode-potential (I-phi(DL)) characteristic. The patterns emerge owing to the interplay of a self-enhancing step in the reaction dynamics and a long-range inhibition by migration currents rather than by diffusion. Theoretical analysis revealed that this self-structuring of the electrode occurs in all electrochemical systems with an S-shaped I-phi(DL) characteristic in wide and well-accessible parameter ranges. This unusual pattern-forming instability in electrochemical systems has all the characteristics of the mechanism proposed by Turing in 1952 in the framework of an early theory of morphogenesis. Our finding might account for structure formation in certain biological systems that have gradients in the electric potential and may open new paths for fabricating patterned electrodes.