The process pp → pℓ+ℓ−p(*), with ℓ+ℓ− a muon or an electron pair produced at midrapidity with mass larger than 110 GeV, has been observed for the first time at the LHC in pp collisions at s=13 TeV. One of the two scattered protons is measured in the CMS-TOTEM precision proton spectrometer (CT-PPS), which operated for the first time in 2016. The second proton either remains intact or is excited and then dissociates into a low-mass state p*, which is undetected. The measurement is based on an integrated luminosity of 9.4 fb−1 collected during standard, high-luminosity LHC operation. A total of 12 μ+μ− and 8 e+e− pairs with m(ℓ+ℓ−) > 110 GeV, and matching forward proton kinematics, are observed, with expected backgrounds of 1.49 ± 0.07 (stat) ± 0.53 (syst) and 2.36 ± 0.09 (stat) ± 0.47 (syst), respectively. This corresponds to an excess of more than five standard deviations over the expected background. The present result constitutes the first observation of proton-tagged γγ collisions at the electroweak scale. This measurement also demonstrates that CT-PPS performs according to the design specifications.[Figure not available: see fulltext.].