We uncover the topological nature of chiral gain and demonstrate how a static electric bias induces topological bandgaps that support unidirectional edge states at the material boundaries. Our findings indicate that topological edge states in this system invariably exhibit dissipative properties. We further show that, by operating outside the topological gap, the chiral gain can be leveraged to engineer boundary-confined lasing modes with orbital angular momentum, locked to the orientation of the applied electric field.