Chiral phosphoric acid-catalyzed couplings of Calkynyl N, N'-di-(tert-butoxycarbonyl)-aminals with β-naphthols led to chiral propargylamines in moderate to high yields with high to excellent enantioselectivity, in which the reactions underwent sequential chiral phosphoric acid-catalyzed in situ formation of N-(tert-butoxycarbonyl)-imines (N-Boc-imines) from the aminals, and 1,2-addition of β-naphthols to the N-Boc-imines. Chiral 1,2-dihydronaphtho[2,1-b]furans and naphtho[2,1-b]furans were prepared with satisfactory results when 10 mol% AgOAc and 20 mol% 2,6-lutidine or 1.2 equiv. of 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) were added to the resulting chiral propargylamines solution, respectively.