  Using $4.479 \times 10^{8}$ $\psi(3686)$ events collected with the BESIII
detector, we search for the decays $\psi(3686) \rightarrow
e^{+}e^{-}\chi_{c0,1,2}$ and $\chi_{c0,1,2} \rightarrow e^{+}e^{-}J/\psi$. The
decays $\psi(3686) \rightarrow e^{+}e^{-}\chi_{c0,1,2}$ and $\chi_{c0,1,2}
\rightarrow e^{+}e^{-}J/\psi$ are observed for the first time. The measured
branching fractions are $\mathcal{B}(\psi(3686) \rightarrow
e^{+}e^{-}\chi_{c0,1,2}) = (11.7 \pm 2.5 \pm 1.0)\times10^{-4}$, $(8.6 \pm 0.3
\pm 0.6)\times10^{-4}$, $(6.9 \pm 0.5 \pm 0.6)\times10^{-4}$, and
$\mathcal{B}(\chi_{c0,1,2} \rightarrow e^{+}e^{-}J/\psi) = (1.51 \pm 0.30 \pm
0.13)\times10^{-4}$, $(3.73 \pm 0.09 \pm 0.25)\times10^{-3}$, $(2.48 \pm 0.08
\pm 0.16)\times10^{-3}$. The ratios of the branching fractions
$\frac{\mathcal{B}(\psi(3686) \rightarrow
e^{+}e^{-}\chi_{c0,1,2})}{\mathcal{B}(\psi(3686) \rightarrow
\gamma\chi_{c0,1,2})}$ and $\frac{\mathcal{B}(\chi_{c0,1,2} \rightarrow
e^{+}e^{-}J/\psi)}{\mathcal{B}(\chi_{c0,1,2} \rightarrow \gamma J/\psi)}$ are
also reported.
