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The concept of off-diagonal geometric phase (GP) has been introduced in order to recover interference information about the geometry of quantal evolution where the standard GPs are not well defined. In this letter, we propose a physical setting for realizing non-Abelian off-diagonal GPs. The proposed non-Abelian off-diagonal GPs can be implemented in a cyclic chain of four qubits with controllable nearest-neighbor interactions. Our proposal seems to be within reach in various nano-engineered systems and therefore opens up for the first experimental test of the non-Abelian off-diagonal GP.