Transition-metal-catalyzed asymmetric allylic alkylation is one of the most powerful and well-known strategies for the construction of C–C bonds; nevertheless, propargylation is elusive and remains far less explored. Here, we report the copper-catalyzed asymmetric propargylic substitution of N-acyl phenylglycine N-hydroxyphthalimide (NHP) esters and racemic propargylic carbonates, which afforded multifunctionalized products bearing a terminal alkyne unit in high yields with good stereoselectivities. Moreover, the product can be readily derivatized into other interesting compounds that have great potential for the exploitation of pharmaceutically relevant molecules.