The copper-catalyzed enantioselective allylic alkylation of terminal alkynes with primary allylic phosphates was developed by the use of a new chiral N-heterocyclic carbene ligand bearing a phenolic hydroxy group at the ortho position of one of the two N-aryl groups. This reaction occurred with excellent gamma-branch regioselectivity and high enantioselectivity, forming a controlled stereogenic center at the allylic/propargylic position. Various terminal alkynes, including silyl, aliphatic, and aromatic alkynes, could be used directly without premetalation of the C(sp)-H bond. On the basis of the results of experiments using an isomeric secondary allylic phosphate, which gave a branched product through a alpha-selective substitution reaction with retention of configuration, a reaction pathway involving 1,3-allylic migration of Cu in a ([sigma + pi]-allyl)copper(III) species is proposed.