[PROBLEMS] To provide a novel method for the allylation of N-acylhydrazones by which enantioselectively allylated N-acylhydrazines can be efficiently obtained.[MEANS FOR SOLVING PROBLEMS] A method for the production of enantioselectively allylated N-acylhydrazines represented by the general formula [3]: ##STR00001## [wherein R.sup.0 is an optionally substituted hydrocarbon group, an optionally substituted heterocyclic group, or --COOR.sup.1 (wherein R.sup.1 is a hydrocarbon group); R.sup.2 is acyl; R.sup.3 and R.sup.4 are each hydrogen, or one of R.sup.3 and R.sup.4 is hydrogen and the other is a hydrocarbon group; and R.sup.5 and R.sup.6 are each independently hydrogen or a hydrocarbon group], characterized by reacting an N-acylhydrazone represented by the general formula [1]: ##STR00002## [wherein R.sup.0 and R.sup.2 are as defined above] with an allylating agent such as allyltrichlorosilane or crotyltrichlorosilane in the presence of a chiral phosphine oxide.