  We report the first observation of the Dalitz decay $\eta' \to \gamma
e^+e^-$, based on a data sample of 1.31 billion $J/\psi$ events collected with
the BESIII detector. The $\eta'$ mesons are produced via the $J/\psi \to \gamma
\eta'$ decay process. The ratio $\Gamma(\eta' \to \gamma e^+
e^-)/\Gamma(\eta'\to\gamma\gamma)$ is measured to be
$(2.13\pm0.09(\text{stat.})\pm0.07(\text{sys.}))\times10^{-2}$. This
corresponds to a branching fraction ${\cal B}(\eta' \to \gamma e^+e^-)= (4.69
\pm0.20(\text{stat.})\pm0.23(\text{sys.}))\times10^{-4}$. The transition form
factor is extracted and different expressions are compared to the measured
dependence on the $e^+e^-$ invariant mass. The results are consistent with the
prediction of the Vector Meson Dominance model.
