A Cu-catalyzed regio- and enantioselective aminoboration of alkylidenecyclopropanes (ACPs) with bis(pinacolato)-diboron (B₂pin₂) and hydroxylamines has been described in this paper, affording the corresponding cyclopropane-containing β-aminoalkylboranes in good yields under mild conditions. Moreover, a catalytic asymmetric variant of this transformation has also been realized by using a copper complex with a (S)-BINAP ligand along with further transformation of the product to give cyclopropane-containing 1,2-aminoalcohols.