Conditions for large non-Gaussianity in two-field slow-roll inflation

16 pages, 6 figures, 1 table.-- PACS number: 98.80.Cq.We study the level of primordial non-Gaussianity in slow-roll two-field inflation. Using an analytic formula for the nonlinear parameter f_NL in the case of a sum or product separable potential, we find that it is possible to generate significant non-Gaussianity even during slow-roll inflation with Gaussian perturbations at Hubble exit. In this paper we give the general conditions to obtain large non-Gaussianity and calculate the level of fine-tuning required to obtain this. We present explicit models in which the non-Gaussianity at the end of inflation can exceed the current observational bound of |f_NL|