A search is performed for electroweak production of a vector-like top quark partner T of charge 2/3 in association with a standard model top or bottom quark, using 2.3 fb−1 of proton-proton collision data at s=13 TeV collected by the CMS experiment at the CERN LHC. The search targets T quarks decaying to a top quark and a Higgs boson in fully hadronic final states. For a T quark with mass above 1 TeV the daughter top quark and Higgs boson are highly Lorentz-boosted and can each appear as a single hadronic jet. Jet substructure and b tagging techniques are used to identify the top quark and Higgs boson jets, and to suppress the standard model backgrounds. An excess of events is searched for in the T quark candidate mass distribution in the data, which is found to be consistent with the expected backgrounds. Upper limits at 95% confidence level are set on the product of the single T quark production cross sections and the branching fraction ℬ (T → t H) , and these vary between 0.31 and 0.93 pb for T quark masses in the range 1000-1800 GeV. This is the first search for single electroweak production of a vector-like T quark in fully hadronic final states.[Figure not available: see fulltext.].