  Using a data sample of $(448.1 \pm 2.9)\times10^6 ~\psi(3686)$ decays
collected at an $e^+ e^-$ center-of-mass energy of $3.686~\rm{GeV}$ by the
BESIII detector at BEPCII, we report an observation of the hindered
electromagnetic Dalitz decay $\psi(3686) \to e^+ e^- \eta_c$ with a
significance of $7.9\sigma$. The branching fraction is determined to be
$\mathcal{B} (\psi(3686) \to e^+ e^- \eta_c) = (3.77 \pm 0.40_{\rm stat.} \pm
0.18_{\rm syst.})\times 10^{-5}$, agreeing well with the prediction of the
vector meson dominance model. This is the first measurement of the
electromagnetic Dalitz transition between the $\psi(3686)$ and the $\eta_c$,
which provides new insight into the electromagnetic properties of this decay,
and offers new opportunities to measure the absolute branching fractions of
$\eta_c$ decays.
