Heterointerfaces have led to the discovery of novel electronic and magnetic states because of their strongly entangled electronic degrees of freedom. Single-phase chromium compounds always exhibit antiferromagnetism following the prediction of the Goodenough-Kanamori rules. So far, exchange coupling between chromium ions via heteroanions has not been explored and the associated quantum states are unknown. Here, we report the successful epitaxial synthesis and characterization of chromium oxide (Cr_{2}O_{3})-chromium nitride (CrN) superlattices. Room-temperature ferromagnetic spin ordering is achieved at the interfaces between these two antiferromagnets, and the magnitude of the effect decays with increasing layer thickness. First-principles calculations indicate that robust ferromagnetic spin interaction between Cr^{3+} ions via anion-hybridization across the interface yields the lowest total energy. This work opens the door to fundamental understanding of the unexpected and exceptional properties of oxide-nitride interfaces and provides access to hidden phases at low-dimensional quantum heterostructures.