χc0ω production in e+e- annihilation through ψ(4160)

We argue that the recent BESIII data on the cross section for the process e(+)e(-) -> chi(c0)omega. in the center-of-mass energy range 4.21-4.42 GeV can be described by the contribution of the known charmoniumlike resonance psi(4160) with the mass of about 4190 MeV. The value of the coupling in the transition psi(4160) -> chi(c0)omega needed for this mechanism is comparable to that in another known similar transition, chi(c0)(2P) -> J/psi omega. The suggested mechanism also naturally explains the relatively small reported value of the cross section for the final states chi(c1)omega and chi(c2)omega above their respective thresholds.