A study of quasi-elastic production of charmed baryons in charged-current interactions of neutrinos with the nuclear emulsion target of CHORUS is presented. In a sample of about 46000 interactions located in the emulsion, candidates for decays of short-lived particles were identified by using new automatic scanning systems and later confirmed through visual inspection. Criteria based both on the topological and kinematical characteristics of quasi-elastic charm production allowed a clear separation between events of this type and those in which charm is produced in deep inelastic processes. A final sample containing 13 candidates consistent with quasi-elastic production of a charmed baryon with an estimated background of 1.7 events was obtained. At the average neutrino energy of 27 GeV the cross-section for the total quasi-elastic production of charmed baryons relative to the vN charged-current cross-section was measured to be sigma(QE)/sigma(CC) = (0.23(-0.06)(+0.12)(stat)(-0.03)(+0.02)(syst)) x 10(-2).