A magnetic domain boundary on the surface of a three-dimensional topological insulator is predicted to host a chiral edge state, but direct demonstration is challenging. We used a scanning superconducting quantum interference device to show that current in a magnetized topological insulator heterostructure (EuS/Bi2Se3) flows at the edge when the Fermi level is gate-tuned to the surface band gap. We further induced micrometer-scale magnetic structures on the heterostructure and detected a chiral edge current at the magnetic domain boundary. The chirality of the current was determined by magnetization of the surrounding domain, and its magnitude by the local chemical potential rather than the applied current. Such magnetic structures provide a platform for detecting topological magnetoelectric effects and may enable progress in quantum information processing and spintronics.