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 root 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 mu(+)/mu(-) 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 gamma gamma collisions at the electroweak scale. This measurement also demonstrates that CT-PPS performs according to the design specifications.