The two-photon transition ψ(3686)→γγJ/ψ is studied in a sample of 1.06×10(8) ψ(3686) decays collected by the BESIII detector. The branching fraction is measured to be (3.1±0.6(stat)(-1.0)(+0.8)(syst))×10(-4) using J/ψ→e(+)e(-) and J/ψ→μ(+)μ(-) decays, and its upper limit is estimated to be 4.5×10(-4) at the 90% confidence level. This work represents the first measurement of a two-photon transition among charmonium states. The orientation of the ψ(3686) decay plane and the J/ψ polarization in this decay are also studied. In addition, the product branching fractions of sequential E1 transitions ψ(3686)→γχ(cJ) and χ(cJ)→γJ/ψ(J=0,1,2) are reported.