Chiral state transfer along closed loops in the vicinity of an exceptional point is one of the many counter-intuitive observations in non-Hermitian physics. The application of this property beyond proof-of-principle, specifically in quantum physics, is an open question. In this work, we demonstrate chiral state conversion between singlet and triplet Bell states through fully-quantum Liouvillian dynamics. Crucially, we demonstrate that this property can be used for the chiral production of Bell states from separable states with a high fidelity and for a large range of parameters. Additionally, we show that the removal of quantum jumps from the dynamics through postselection can result in near-perfect Bell states from initially separable states. Our work paves the way to a novel type of quantum control and a potential application of non-Hermitian physics in quantum information processing.