We have found that significant levels of enantioselectivity are obtained in the 1,3-dipolar cycloadditions of 2-benzopyrylium-4-olate using chiral 2,6-bis(oxazolinyl)pyridine (Pybox)-rare earth metal triflate complexes as chiral Lewis acid catalysts. The reactions with benzyloxyacetaldehyde derivatives catalyzed by Sc(III)-Pybox-i-Pr (10 mol %) proceeded to give endo-adducts selectively with high enantioselectivity (up to 93% ee). The reaction with benzyl pyruvate under similar conditions gave an exo-adduct selectively with 87% ee. In the reaction with 3-acryloyl-2-oxazolidinone, Yb(III)-Pybox-Ph was found to be effective in providing an exo-adduct with extremely high enantioselectivity (98% ee).