A bstract Results are reported from a search for the lepton flavor violating decay τ → 3 μ in proton-proton collisions at $$ \sqrt{\mathrm{s}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt></mml:math> = 13 TeV. The data sample corresponds to an integrated luminosity of 33.2 fb − 1 recorded by the CMS experiment at the LHC in 2016. The search exploits τ leptons produced in both W boson and heavy-flavor hadron decays. No significant excess above the expected background is observed. An upper limit on the branching fraction ℬ( τ → 3 μ ) of 8 . 0 × 10 − 8 at 90% confidence level is obtained, with an expected upper limit of 6 . 9 × 10 − 8 .