The possibility of using exchange interactions to manipulate the spin state of an antiferromagnetic nanostructure is explored using ab initio calculations. By considering M (M = Mn, Fe, Co) mono-atomic chains supported on Cu₂N islands on a Cu(001) surface as a model system, it is demonstrated that two indistinguishable Néel states of an antiferromagnetic chain can be tailored into a preferred state by the exchange interaction with a magnetic STM tip. The magnitude and direction of the anisotropy for antiferromagnetic chains can also be tuned by exchange coupling upon varying the tip-chain separation.