  We show how a fermionic quantum gas in an optical lattice and coupled to the
field of an optical cavity can self-organize into a state in which the
spontaneously emerging cavity field amplitude induces an artificial magnetic
field. The fermions form either a chiral insulator or a chiral liquid carrying
edge currents. The feedback mechanism via the cavity field enables robust and
fast switching of the edge currents and the cavity output can be employed for
non-destructive measurements of the atomic dynamics.
