Terminal alkynes have become one of the most versatile building blocks for C-C bond construction in the past few decades, and they are usually considered to convert to acetylides before further transformations. In this study, a novel direct nucleophilic addition mode for Cu(I)-catalyzed cross-coupling of terminal alkynes and N-tosylhydrazones to synthesize chiral allenes is proposed, and it was investigated by density functional theory with the M11-L density functional. Three different reaction pathways were considered and investigated. The computational results show that the proposed reaction pathway, which includes direct nucleophilic attack of protonated acetylene, deprotonation of the vinyl cation, and catalyst regeneration, is the most favorable pathway. Another possible deprotonation-carbenation-insertion pathway is shown to be unfavorable. The direct nucleophilic addition step is the rate- and enantioselectivity-determining step in the catalytic cycle. Noncovalent interaction analysis shows that the steric effect between the methyl group of the carbene moiety and the naphthalyl group of the bisoxazoline ligand is important to control the enantioselectivity. In addition, calculation of a series of chiral bisoxazoline ligands shows that a bulky group on the oxazoline ring is favorable for high enantioselectivity, which agrees with experimental observations. Moreover, copper acetylides are stable, and their generation is a favorable pathway in the absence of chiral bisoxazoline ligands.