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We observe for the first time the process $e^{+}e^{-} \rightarrow \eta h_c$with data collected by the BESIII experiment. Significant signals are observedat the center-of-mass energy $\sqrt{s}=4.226$ GeV, and the Born cross sectionis measured to be $(9.5^{+2.2}_{-2.0} \pm 2.7)$ pb. Evidence for $\eta h_c$ isobserved at $\sqrt{s}=4.358$ GeV with a Born cross section of$(10.0^{+3.1}_{-2.7} \pm 2.6)$ pb, and upper limits on the production crosssection at other center-of-mass energies between 4.085 and 4.600 GeV aredetermined.

Observation of $e^{+}e^{-} \to \eta h_{c}$ at center-of-mass energies from 4.085 to 4.600 GeV