The nuclear emulsion target of the CHORUS detector was exposed to the wide-band neutrino beam of the CERN SPS of 27 GeV average neutrino energy from 1994 to 1997. In total, about 100 000 charged-current (CC) neutrino interactions with at least one identified muon were located in the emulsion target and fully reconstructed, using newly developed automated scanning systems. Charmed particles were searched for by a program recognizing particle decays. The observation of the decay in nuclear emulsion makes it possible to select a sample with very low background and minimal kinematical bias. In all, 2013 CC interactions with a charmed hadron candidate in the final state were selected and confirmed through visual inspection. The charm production rate induced by neutrinos relative to the CC cross-section is measured to be sigma(nu N-mu -> mu-CX)/sigma(CC) = (5.75 +/- 0.32(stat) +/- 0.30(syst))%. The charm production cross-section as a function of neutrino energy is also obtained. The results are in good agreement with previous measurements. The charm-quark hadronization produces the following charmed hadrons with relative fractions (in %): f(D)(0) = 43.7 +/- 4.5, f(Lambda c)(+) = 19.2 +/- 4.2, f(D)(+) = 25.3 +/- 4.2 and f(Ds)(+) = 11.8 +/- 4.7.