[reaction: see text] An efficient three-component coupling of aldehyde, alkyne, and amine to generate propargylamines has been effected under microwave irradiation in water using only CuI catalyst without the noble metal cocatalyst. This method has proved to be applicable to a wide range of substrates. In addition, the preliminary experiment using (S)-proline methyl ester as a chiral source demonstrated that it could be developed to be a direct and highly diastereoselective method for construction of chiral propargylamines.