A new chiralbisphosphine ligand ((R)-2-diphenylphosphino-2′-diphenylphosphinomethyl-1,1′-binaphthyl) was synthesized from enantiomerically pure (R)-1,1′-binaphthalene-2,2′-diol. Rhodium(I) complexes of this bisphosphine ligand have been used as catalysts for asymmetrichydrogenation of α-alkylstyrenes to give the corresponding aromatic hydrocarbons in up to 77% ee.