This Letter reports on a study of trimuon events induced by neutrino interactions in the CHORUS calorimeter exposed to the CERN SPS wide-band v(mu) beam. Among the multimuon events produced in the calorimeter, 42 mu(-) mu(-) mu(+) events were selected and their kinematical properties investigated. In the past, several groups collected a sample of about one hundred events of this type but their source was largely unknown. Taking advantage of experimental data presently available on the production and muonic branching ratios of light neutral mesons and resonances, we make absolute predictions for the expected rates in our experiment. Detailed Monte Carlo simulations described in this article show that more than half of the trimuon events can be attributed to this source. Muons from pi- and K- decays in charm dimuon events are responsible for an additional approximate to 25% contribution to the total mu(-)mu(-)mu(+) rate. The remaining 25% of events are likely to come from the internal bremsstrahlung of virtual photons into a muon pair. Associated-charm production with subsequent decays of both charmed particles into muons is a negligible source of trimuon events. (C) 2004 Elsevier B.V. All rights reserved.