Multiple inflation is a model based on N=1 supergravity wherein there are sudden changes in the mass of the inflaton because it couples to flat direction scalar fields which undergo symmetry breaking phase transitions as the universe cools. The resulting brief violations of slow-roll evolution generate a non-gaussian signal which we find to be oscillatory and yielding f_NL ~ 5-20. This is potentially detectable by e.g. Planck but would require new bispectrum estimators to do so. We also derive a model-independent result relating the period of oscillations of a phase transition during inflation to the period of oscillations in the primordial curvature perturbation generated by the inflaton.