Reactive transport in porous media is described by (a system of) non-linear differential equations. Typically, the parameters entering these equations are either under-specified by data (e.g., hydraulic conductivity, macroscopic velocity) or cannot be measured on a required scale in principle (e.g., the dynamic behavior of interfacial surfaces between reacting components, pore-scale velocity). In recent decades stochastic methods, which treat such parameters as random fields, have emerged as a powerful tool for dealing with uncertainty inherent in modeling subsurface phenomena. Monte Carlo simulations and Moment Differential Equations (MDE) methods are used most often in stochastic hydrogeology. The comparative strengths and weaknesses of both approaches are well understood. By contrast, so-called PDF approaches, which are based on deriving (conditional) probability density functions for the corresponding stochastic flow and transport equations, have received virtually no attention. Yet their advantages for analyzing reactive transport are manifold. Unlike most MDE approaches, they do not linearize the governing equations and provide a natural framework for analyzing rare events that are crucial for risk assessment studies. We derive a general PDF method for advective transport of a contaminant undergoing a heterogeneous, nonlinear, chemical reaction. We further demonstrate the applicability of this approach and contrast it with MDE methods.