We present a model based on an SU(3) family symmetry providing a full description of quark and lepton masses and mixing angles. CP is spontaneously broken in the flavour sector reproducing the observed results of the Jarlskog invariant in the CKM mixing matrix. Moreover, our model predicts the amount of CP violation to be expected in the neutrino sector. Furthermore, this approach solves the Supersymmetric CP and FCNC problems in a gravity mediation scenario. The symmetry predicts the structure of the squark and slepton mass matrices and this will be checked in future experiments.