Antiferromagnetic chains with an odd number of spins are known to undergo a transition from an antiparallel to a spin-flop configuration when subjected to an increasing magnetic field. We show that in the presence of an anisotropy favoring alignment perpendicular to the field, the spin-flop state appears for both weak and strong field, the antiparallel state appearing for intermediate fields.Both transitions are second order, the configuration varying continuously with the field intensity. Such re-entrant transition is robust with respect to quantum fluctuations and it might be observed in different types of nanomagnets.