The cross section of the process $e^+e^- rightarrow omega chi_{c0}$ is measured at center-of-mass energies from $sqrt{s} =$ 4.178 to 4.278 GeV using a data sample of 7 fb$^{-1}$ collected with the BESIII detector operating at the BEPCII storage ring. The dependence of the cross section on $sqrt{s}$ shows a resonant structure with mass of $(4218.5pm1.6(text{stat.})pm4.0(text{syst.}))$ MeV/$c^2$ and width of $(28.2pm3.9(text{stat.})pm1.6(text{syst.}))$ MeV, respectively. This observation confirms and improves upon the result of a previous study. The angular distribution of the $e^+e^- rightarrow omega chi_{c0}$ process is extracted for the first time.
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