  Using a total of $5.25~{\rm fb}^{-1}$ of $e^{+}e^{-}$ collision data with
center-of-mass energies from 4.236 to 4.600 GeV, we report the first
observation of the process $e^{+}e^{-}\to \eta\psi(2S)$ with a statistical
significance of $5\sigma$. The data sets were collected by the BESIII detector
operating at the BEPCII storage ring. We measure the yield of events integrated
over center-of-mass energies and also present the energy dependence of the
measured cross section.
