A search is made for a vectorlike T quark decaying into a Higgs boson and a top quark in 13 TeV protonproton collisions using the ATLAS detector at the Large Hadron Collider with a data sample corresponding to an integrated luminosity of 139 fb???1. The Higgs-boson and top-quark candidates are identified in the all-hadronic decay mode, where H - bb ?? and t - bW - bqq??0 are reconstructed as large-radius jets. The candidate Higgs boson, top quark, and associated B hadrons are identified using tagging algorithms. No significant excess is observed above the background, so limits are set on the production cross section of a singlet T quark at 95% confidence level, depending on the mass mT and coupling ??T of the vectorlike T quark to Standard Model particles. In the considered mass range between 1.0 and 2.3 TeV, the upper limit on the allowed coupling values increases with mT from a minimum value of 0.35 for 1.07 < mT < 1.4 TeV to 1.6 for mT 1/4 2.3 TeV.