ATLAS and CMS have reported an excess in the flavour violating decay of the Higgs
boson, $h \to \mu \tau$. I this talk, I show that this result can be accommodated through
a mixing of the Higgs with a flavon, the field responsible for generating the Yukawa
matrices in the lepton sector. We employ a discrete version of the Froggatt-Nielsen
mechanism at the TeV scale, with only leptons and the flavon transforming non–trivially
under the corresponding symmetry group. Non–observation of charged lepton flavour
violation in other processes imposes important constraints on the model, which
we find to be satisfied in substantial regions of parameter space.