Tertiary propargylic sulfones are of significant importance in organic synthesis and medicinal chemistry, but to date no general asymmetric synthesis approach has been developed. Here we disclose a versatile copper‐catalyzed sulfonylation of propargylic cyclic carbonates using sodium sulfinates allowing to construct propargylic sulfones featuring elusive quaternary stereocenters. This method provides the first successful example of enantioselective propargylic sulfonylation, features high asymmetric induction, wide functional group tolerance and scalability, and attractive product diversification.