The asymmetric addition of silylacetylenes to 1,1-disubstituted allenes proceeded in the presence of a cobalt/chiral bisphosphine ligand to give the corresponding enynes with high enantioselectivity. The results of deuterium-labeling experiments indicated that a hydrogen atom at the chiral center is originated from the terminal alkyne, and they were in good agreement with the proposed catalytic cycle where enantioselectivity is determined by the reaction of the proposed π-allylcobalt intermediate with the terminal alkyne.