We propose an entirely new class of particle physics models of inflation based on the phase transition associated with the spontaneous breaking of family symmetry responsible for the generation of the effective quark and lepton Yukawa couplings. We show that the Higgs fields responsible for the breaking of family symmetry, called flavons, are natural candidates for the inflaton field in new inflation, or the waterfall fields in hybrid inflation. This opens up a rich vein of possibilities for inflation, all linked to the physics of flavour, with interesting cosmological and phenomenological implications. Out of these, we discuss two examples which realise flavon inflation: a model of new inflation based on the discrete non-Abelian family symmetry group A_{4} or Delta_{27}, and a model of hybrid inflation embedded in an existing flavour model with a continuous SU(3) family symmetry. With the inflation scale and family symmetry breaking scale below the Grand Unification Theory (GUT) scale, these classes of models are free of the monopole (and similar) problems which are often associated with the GUT phase transition.

12 pages, 3 figures. References added. Matches published version