The method of Morales and Ramis determines whether a given Hamiltonian system is non-integrable. We apply this method to Friedmann Robertson Walker models with a self-interacting scalar field and cosmological constant. It is shown that, with the exception of a set of measure zero, these models are non-integrable. Our results complement those of Helmi and Vucetich who used the Painlevé property to find integrable models within this class.
