We present the first detection of ^ { 12 } CO J=2 \rightarrow 1 and ^ { 12 } CO J=1 \rightarrow 0 emission from the LBV AG Carinae . We show that 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 \simeq 7 km s ^ { -1 } . 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 . Both detected CO lines are characterised by a pseudo-gaussian profile of FWHM \simeq 15 km s ^ { -1 } , indicating a slowly expanding region of molecular gas in close proximity to the hot central star . We have explored two possible scenarios to explain the observed profile : a circumstellar envelope , similar to carbon stars , or a circumstellar disk . The option of the circumstellar disk is preferable because : 1 ) 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 2 ) it provides the conditions of density and shielding necessary for the survival of the CO molecules in proximity to such a hot star ( T _ { eff } \simeq 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 CO-mass of 6.5 \times 10 ^ { -3 } M _ { \odot } . We also estimate that the CO fraction is \simeq 2.3 \times 10 ^ { -3 } of the total mass of molecular gas , which then would amount to 2.8 M _ { \odot } . This is smaller , but still comparable with the mass of ionized gas present in the circumstellar environment ( 4.2 M _ { \odot } ) , 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 .