The J/ψ →μ+μ−μ+μ− decay has been observed with a statistical significance in excess of five standard deviations. The analysis is based on an event sample of proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the CMS experiment in 2018 and corresponding to an integrated luminosity of 33.6 fb−1. Normalizing to the J/ψ →μ+μ− decay mode leads to a branching fraction of [10.1+3.3−2.7(stat) ±0.4(syst)] ×10−7, a value that is consistent with the standard model prediction.