  Based on $(10087 \pm 44)\times10^6$ $J/\psi$ events collected with the BESIII
detector at BEPCII, the double Dalitz decay $\eta'\to e^+e^-e^+e^-$ is observed
for the first time via the $J/\psi\to\gamma\eta'$ decay process. The
significance is found to be 5.7$\sigma$ with systematic uncertainties taken
into consideration. Its branching fraction is determined to be
$\mathcal{B}(\eta'\to e^+ e^- e^+ e^-)
=(4.5\pm1.0(\mathrm{stat.})\pm0.5(\mathrm{sys.})) \times 10^{-6}$.
