(-)-Quinine-catalyzed intramolecular oxo-Michael addition (IMA) of 7-hydroxy-5-methoxy-8-tigloylcoumarins was developed for the enantioselective construction of 2,3-dimethyl-4-chromanone systems in the context of the asymmetric synthesis of anti-HIV-1 active Calophyllum coumarins. Combination of the IMA and MgI(2)-assisted demethylation of the 5-methoxy group along with isomerization of the formed chromanone systems as key steps successfully led to the concise synthesis of (+)-inophyllum B and (+)-calanolide A, possible candidates for AIDS drugs. Further examination of the asymmetric IMA with cinchona alkaloids lacking a methoxy group on the quinoline skeleton suggested the influence of the methoxy substituent on stereoselectivity at the stereogenic centers of the chromanone systems.