For decades, simplified statistical models of neural behaviors have been providing insights into the nature of pattern recognition, associative memory, and learning. Interestingly, the models developed for neural networks are equally applicable -- if not more so -- for describing the potential behaviors of certain natural and synthetic chemical systems. Recently, a variety of neural-like systems have been implemented within cell-free biochemistry. This leads us to ask, "How smart can a micron-sized bag of chemicals be?” At this scale, stochastic aspects of molecular behavior comes to the fore. Rather than being an impediment, we show that stochastic chemical kinetics provides a natural way for cell-scale systems to represent probability distributions generatively, and that when presented with known information, these chemical networks perform exact inference by generating conditional distributions. Our arguments make use of an exact mathematical connection between certain stochastic chemical reaction networks and the classical Boltzmann machine model of neural computation. Potential implementation using dynamic DNA nanotechnology will be discussed.