Using $4.48 times 10^{8}$ $psi(3686)$ events collected with the BESIII detector, we search for the decays $chi_{cJ} rightarrow mu^{+}mu^{-}J/psi$ through the radiative decays $psi(3686) rightarrow gammachi_{cJ}$, where $J=0,1,2$. The decays $chi_{c1,2} rightarrow mu^{+}mu^{-}J/psi$ are observed, and the corresponding branching fractions are measured to be $mathcal{B}(chi_{c1} rightarrow mu^{+}mu^{-}J/psi) = (2.51 pm 0.18 pm 0.20)times10^{-4}$ and $mathcal{B}(chi_{c2} rightarrow mu^{+}mu^{-}J/psi) = (2.33 pm 0.18 pm 0.29)times10^{-4}$, where the first uncertainty is statistical and the second one systematic. No significant $chi_{c0} rightarrow mu^{+}mu^{-}J/psi$ decay is observed, and the upper limit on the branching fraction is determined to be $2.0times10^{-5}$ at 90% confidence level. Also, we present a study of di-muon invariant mass dependent transition form factor for the decays $chi_{c1,2} rightarrow mu^{+}mu^{-}J/psi$.
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