Using 4.48 × 10 8 ψð3686Þ events collected with the BESIII detector, we search for the decays χ cJ → μ þ μ − J=ψ through the radiative decays ψð3686Þ → γχ cJ , where J ¼ 0, 1, 2. The decays χ c1;2 → μ þ μ − J=ψ are observed, and the corresponding branching fractions are measured to be Bðχ c1 → μ þ μ − J=ψÞ ¼ ð2.51 AE 0.18 AE 0.20Þ × 10 −4 and Bðχ c2 → μ þ μ − J=ψÞ ¼ ð2.33 AE 0.18 AE 0.29Þ × 10 −4 , where the first uncertainty is statistical and the second one systematic. No significant χ c0 → μ þ μ − J=ψ decay is observed, and the upper limit on the branching fraction is determined to be 2.0 × 10 −5 at 90% confidence level. Also, we present a study of dimuon invariant mass dependent transition form factor for the decays χ c1;2 → μ þ μ − J=ψ.