Non-linear effects, present in all inflation models, will cause the primordial perturbation spectrum to be non-Gaussian. While these effects are small, CMB data are getting sufficiently accurate that we might well expect to detect them in the near future with WMAP and Planck, providing us with new information about the early universe. In this talk I will discuss the formalism we developed to deal with the required non-linearity during inflation. Applying it to single-field inflation shows that there the non-Gaussianity is unobservably small. However, next I will apply the formalism to general multiple-field inflation and derive an analytic expression for the bispectrum. From this I show that the non-linear super-horizon evolution of the combined adiabatic and isocurvature modes during multiple-field inflation can lead to observably large non-Gaussianity. While everything can be computed exactly semi-analytically, I also show how, without doing the full calculation, one can give a simple estimate for the magnitude in terms of background quantities. Specific examples are worked out.