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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 - 4.42GeV 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 thetransition $\psi(4160) \to \chi_{c0} \, \omega$ needed for this mechanism iscomparable to that in another known similar transition $\chi_{c0}(2P) \toJ/\psi \, \omega$. The suggested mechanism also naturally explains the reportedrelative small value of the cross section for the final states $\chi_{c1} \,\omega$ and $\chi_{c2} \, \omega$ above their respective thresholds.

$\chi_{c0} \, \omega$ production in $e^+e^-$ annihilation through $\psi(4160)$