We study the spreading of viscous drops on a solid substrate, taking into account the effects of thermal fluctuations in the fluid momentum. A nonlinear stochastic lubrication equation is derived, and studied using numerical simulations and scaling analysis. We show that asymptoically spreading drops admit self-similar shapes, whose average radii can increase at rates much faster than these predicted by Tanner's law. We discuss the physical realizablility of our results for thin molecular and complex fluid films, and predict that such phenomenon can in principal be observed in various flow geometries.