A detailed study of the direct catalytic asymmetric conjugate addition of terminal alkynes to α,β-unsaturated thioamides is described. A soft Lewis acid/hard Brønsted base cooperative catalyst, comprising [Cu(CH(3)CN)(4)]PF(6), bisphosphine ligand, and Li(OC(6)H(4)-p-OMe) simultaneously activated both substrates to compensate for the low reactivity of copper alkynylide. A series of control experiments revealed that the intermediate copper-thioamide enolate functioned as a Brønsted base to generate copper alkynylide from the terminal alkyne, thus driving the catalytic cycle through an efficient proton transfer between substrates. These findings led to the identification of a more convenient catalyst using potassium hexamethyldisilazane (KHMDS) as the Brønsted base, which was particularly effective for the reaction of silylacetylenes. Divergent transformation of the thioamide functionality and a concise enantioselective synthesis of a GPR40 receptor agonist AMG-837 highlighted the synthetic utility of the present catalysis.