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