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 -> tau tau, and H -> ZZ decay modes, and signatures with a single lepton and a b (b) over bar pair, targeting the H -> b (b) over bar decay, are combined with a reinterpretation of a measurement in the H -> gamma gamma 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).