A search for the standard model Higgs boson decaying to a charm quark-antiquark pair, H → cc, produced in association with a top quark-antiquark pair (ttH) is presented. The search is performed with data from proton-proton collisions at √ s = 13 TeV, corresponding to an integrated luminosity of 138/fb. Advanced machine learning techniques are employed for jet flavor identification and event classification. The Higgs boson decay to a bottom quark-antiquark pair is measured simultaneously and the observed ttH (H → bb) event rate relative to the standard model expectation is 0.91 +0.26−0.22. The observed (expected) upper limit on the product of production cross section and branching fraction σ(ttH) B(H → cc) is 0.11 (0.13) pb at 95% confidence level, corresponding to 7.8 (8.7) times the standard model prediction. When combined with the previous search for H → cc via associated production with a W or Z boson, the observed (expected) 95% confidence interval on the Higgs-charm Yukawa coupling modifier, κc, is |κc| < 3.5 (2.7), the most stringent constraint to date.