Doping of CuGeO3 by 2% Co was found to cause a new magnetic resonance, which has anomalous polarization characteristics. In the Faraday geometry, where a microwave field B ω is directed along certain crystallographic directions, this mode is suppressed, which indicates that the character of magnetic oscillations in this mode differs strongly from standard spin precession. This resonance coexists with the EPR on Cu2+ chains and is likely to be caused by an unknown collective mode of magnetic oscillations of an antiferromagnetic quantum S = 1/2 spin chain.