I describe a recently derived stochastic approach to inflaton dynamics which can address some serious problems associated with conventional inflationary theory. Using this theory I derive an exact solution to the stochastic dynamics for the case of a $λϕ^4$ potential and use it to study the generated primordial density fluctuations. It is found that on both sub and super-horizon scales the theory predicts gaussian fluctuations to a very high accuracy along with a near scale-invariant spectrum. Of most interest is that the amplitude constraint is found to be satisfied for $λ\sim 10^{-5}$ rather than $λ\sim 10^{-14}$ of the conventional theory. This represents a dramatic easing of the fine-tuning constraints, a feature likely to generalize to a wide range of potentials.

5 pages in Latex (uses Revtex), no figures. Minor changes to the text only