While the properties of the observed Higgs boson agree with the Standard Model predictions, the hierarchy of fermion masses lacks an explanation within the model. In this work, we consider a fresh approach to this problem, involving a different Higgs doublet responsible for each quark mass. We construct a model with a gauged, non-anomalous U(1) family symmetry that fixes which fermion couples to which doublet with an O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(1) Yukawa coupling. The hierarchy of masses is generated by the hierarchy of vacuum expectation values of the Higgs fields. The model generically predicts a light, weakly coupled pseudoscalar. We verify that the model satisfies constraints from flavour changing neutral currents, Higgs phenomenology and electroweak precision tests.