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