  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
$(4218.5\pm1.6(\text{stat.})\pm4.0(\text{syst.}))$ MeV/$c^2$ and width of
$(28.2\pm3.9(\text{stat.})\pm1.6(\text{syst.}))$ 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.
