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A direct search for the standard model Higgs boson decaying to a pair of charm quarks is presented. Associated production of the Higgs and Z bosons, in the decay mode ZH -> l(+)l(-) cc is studied. A data set with an integrated luminosity of 36.1 fb(-1) of pp collisions at root s = 13TeV recorded by the ATLAS experiment at the LHC is used. The H -> cc signature is identified using charm-tagging algorithms. The observed (expected) upper limit on sigma(pp -> ZH) x B(H -> cc) is 2.7 (3.9(-2.1)(+2.1) ) pb at the 95% confidence level for a Higgs boson mass of 125 GeV, while the standard model value is 26 fb.