Enantioselective alkynylation of cyclic N-sulfonyl α-ketiminoesters with terminal alkynes was developed by using an Ni(ClO4)2/(R)-DTBM-Segphos complex as a catalyst. A range of propargylic amides bearing quaternary stereocenters were afforded in excellent enantioselectivities (up to 97% ee). Theoretical studies revealed that this reaction proceeded via a Friedel-Crafts-type reaction pathway.