  We present the first detection of 12 CO J=2->1 and 12 CO J=1->0 emission from
the LBV AG Carinae. AG Carinae resides in a region which is very rich in
molecular gas with complex motions. We find evidence of a slow outflow of
molecular gas, expanding at ~ 7 km/s. This emission appears spatially
unresolved. We argue that it is spatially localised, rather than extended, and
possibly associated with the immediate circumstellar region of AG Carinae. Does
it originate from a circumstellar envelope, similar to carbon stars, or from a
circumstellar disk? The option of the circumstellar disk is preferable because
it is consistent with additional independent indications for the existence of
wind asymmetries in close proximity to the central star, found from
spectropolarimetry and analysis of the UV and optical line profiles, and it
provides the conditions of density and shielding necessary for the survival of
the CO molecules in proximity to such a hot star (Teff ~ 14000 K - 20000 K). In
the assumption that the CO emission originated when AG Carinae was in an
evolved state, we derive a lower limit to the mass of molecular gas of 2.8
solar masses. This is smaller, but still comparable with the mass of ionized
gas present in the circumstellar environment (4.2 solar masses), with the
implication that the molecular gas fraction can contribute significantly to the
overall mass lost from the central star in its post main sequence evolution.
