  The process $e^{+}e^{-}\to \eta^{\prime} J/\psi$ is observed for the first
time with a statistical significance of $8.6\sigma$ at center-of-mass energy
$\sqrt{s} = 4.226$ GeV and $7.3\sigma$ at $\sqrt{s} = 4.258$ GeV using data
samples collected with the BESIII detector. The Born cross sections are
measured to be $(3.7 \pm 0.7 \pm 0.3)$ and $(3.9 \pm 0.8 \pm 0.3)$ pb at
$\sqrt{s} = 4.226$ and $4.258$ GeV, respectively, where the first errors are
statistical and the second systematic. Upper limits at the 90% confidence level
of the Born cross sections are also reported at other 12 energy points.
