1,1'-Bi-2-naphthol in combination with ZnEt2, Ti(O(i)Pr)4, and dicyclohexylamine have been employed to catalyze asymmetric alkyne addition to an ynal to synthesize optically active propargylic alcohols containing two alkyne functions with excellent yields and enantioselectivities. These chiral alcohols are readily converted to the corresponding optically active propargyl 2,4-hexadienyl ethers. These diene-diyne substrates are found to undergo a highly chemoselective and stereoselective domino Pauson-Khand and Diels-Alder cycloaddition catalyzed by [RhCl(CO)2]2 under CO to generate a class of tetracyclic compounds with high enantiomeric purity. This is a very efficient method for the asymmetric synthesis of polycyclic compounds.