We consider a modification of electrodynamics by an additional light massive vector field, interacting with the photon via Chern-Simons-like coupling. This theory predicts observable effects for the experiments studying the propagation of light in an external magnetic field, very similar to those, predicted by theories of axion and axion-like particles. We discuss a possible microscopic origin of this theory from a theory with non-trivial gauge anomaly cancellation between massive and light particles (including, for example, millicharged fermions). Due to the conservation of the gauge current, the production of the new vector field is suppressed at high energies. As a result, this theory can avoid both stellar bounds (which exist for axions) and the bounds from CMB considered recently, allowing for positive results in experiments like ALPS, LIPPS, OSQAR, PVLAS-2, BMV, Q&A, etc. (C) 2007 Elsevier B.V. All rights reserved.