Chiral Lewis acid-catalyzed asymmetric alcohol addition reactions to cyclic carbonyl ylides generated from N-(α-diazocarbonyl)-2-oxazolidinones featuring a dual catalytic system are reported. Construction of a chiral quaternary heteroatom-substituted carbon center was accomplished in which the unique heterobicycles were obtained in good yields with high stereoselection. The alcohol adducts were successfully converted to optically active oxazolidine-2,4-diones by hydrolysis. Mechanistic studies by DFT calculations revealed that alcohols could be activated by Lewis acids, enabling enantioselective protonation of the carbonyl ylides.