I will introduce the novel phenomenon of CP-violating inflation which arises in models with several scalar doublets. The inert (without vacuum expectation value) doublets have a non-minimal coupling to gravity and play the role of the inflaton. I allow for this coupling to be complex, thereby introducing CP-violation - a necessary source of the baryon asymmetry - in the Higgs–inflaton couplings. I discuss the inflationary dynamics of such a model and show how the CP-violation is imprinted on the particle asymmetries after inflation in the hot big bang universe.