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

We observe for the first time the process $e^{+}e^{-} rightarrow eta h_c$ with data collected by the BESIII experiment. Significant signals are observed at the center-of-mass energy $sqrt{s}=4.226$ GeV, and the Born cross section is measured to be $(9.5^{+2.2}_{-2.0} pm 2.7)$ pb. Evidence for $eta h_c$ is observed 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 cross section at other center-of-mass energies between 4.085 and 4.600 GeV are determined.