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-→χc0ω in the center-of-mass energy range 4.21-4.42 GeV can be described by the contribution of the known charmoniumlike resonance ψ(4160) with the mass of about 4190 MeV. The value of the coupling in the transition ψ(4160)→χc0ω needed for this mechanism is comparable to that in another known similar transition, χc0(2P)→J/ψω. The suggested mechanism also naturally explains the relatively small reported value of the cross section for the final states χc1ω and χc2ω above their respective thresholds.