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Abstract The inclusive hadroproduction of a Higgs boson and of a jet, featuring large transverse momenta and well separated in rapidity, is proposed as a novel probe channel for the manifestation of the Balitsky–Fadin–Kuraev–Lipatov (BFKL) dynamics. Using the standard BFKL approach, with partial inclusion of next-to-leading order effects, predictions are presented for azimuthal Higgs-jet correlations and other observables, to be possibly compared with experimental analyses at the LHC and with theoretical predictions obtained in different schemes.