  We propose a new mechanism for topological superconductivity based on an
antiferromagnetically ordered chain of magnetic atoms on the surface of a
conventional superconductor. In a weak Zeeman field, a supercurrent in the
substrate generates a staggered spin-current, which converts the preexisting
topologically-unprotected Shiba states into Majorana fermions (MFs). The two
experimental knobs can be finely tuned providing a platform with enhanced
functionality for applications. Remarkably, the electronic spin-polarization of
the arising edge MF wavefunctions depends solely on the parity of the number of
magnetic moments, which can serve as a distinctive signature of the MFs. We
introduce the basic concepts within a minimal model and make contact with
experiments by a microscopic analysis based on the Shiba states.
