We report a facile method to synthesize stereodefined quaternary centers from reactions of arynes and related strained intermediates using beta-ketoester-derived substrates. The conversion of beta-ketoesters to chiral enamines is followed by reaction with in situ generated strained arynes or cyclic alkynes. Hydrolytic workup provides the arylated or alkenylated products in enantiomeric excesses as high as 96%. We also describe the one-pot conversion of a beta-ketoester substrate to the corresponding enantioenriched alpha-arylated product. Computations show how chirality is transferred from the N-bound chiral auxiliary to the final products. These are the first theoretical studies of aryne trapping by chiral nucleophiles to set new stereocenters. Our approach provides a solution to the challenging problem of stereoselective beta-ketoester arylation/alkenylation, with formation of a quaternary center.