  We measure the Born cross section for the reaction $e^{+}e^{-} \rightarrow
\eta h_c$ from $\sqrt{s} = 4.129$ to $4.600$~GeV using data sets collected by
the BESIII detector running at the BEPCII collider. A resonant structure in the
cross section line shape near 4.200~GeV is observed with a statistical
significance of 7$\sigma$. The parameters of this resonance are measured to be
\MeasMass\ and \MeasWidth, where the first uncertainties are statistical and
the second systematic.
