A novel homochiral zeolite-like metal–organic framework (ZMOF), [(Cu4I4) (dabco)2]·[Cu2(bbimb)]·3DMF (JLU-Liu23, dabco =1,4-diazabicyclo[2.2.2]-octane, H2bbimb =1,3-bis(2-benzimidazol)benzene, DMF = N,N-dimethylformamide), has been successfully constructed to host unprecedented DNA-like [Cu2(bbimb)]n polymers with double-helicity. The host–guest chirality interplay permitted the induced formation of an unusual gyroid MOF with homochirality and helical channels in the framework for the first time, JLU-Liu23. Importantly, the enantiomeric pairs (23P, 23M) can be promoted and isolated in the presence of appropriate chiral inducing agents, affording enantioselective separation of chiral molecules as well as small gas molecules.