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, y_t; the Higgs boson coupling to vector bosons, g_HVV; 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 bb¯ pair, targeting the H → bb¯ decay, are combined with a reinterpretation of a measurement in the H → γγ channel to constrain y_t. For a standard model-like value of g_HVV, the data favor positive values of y_t and exclude values of y_t below about -0.9y_t^SM.