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A search is presented for the production of a Higgs boson in association with a single top quark, based on data collected in 2016 by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV, which corresponds to an integrated luminosity of 35.9  fb−1. The production cross section for this process is highly sensitive to the absolute values of the top quark Yukawa coupling, yt; the Higgs boson coupling to vector bosons, gHVV; and, uniquely, their relative sign. Analyses using multilepton signatures, targeting H→WW, H→ττ, and H→ZZ decay modes, and signatures with a single lepton and a b¯b pair, targeting the H→b¯b decay, are combined with a reinterpretation of a measurement in the H→γγ channel to constrain yt. For a standard model-like value of gHVV, the data favor positive values of yt and exclude values of yt below about −0.9ytSM.