  We study a stochastic system of $N$ interacting particles which models
bimolecular chemical reaction-diffusion. In this model, each particle $i$
carries two attributes: the spatial location $X_t^i\in \mathbb{T}^d$, and the
type $\Xi_t^i\in \{1,\cdots,n\}$. While $X_t^i$ is a standard (independent)
diffusion process, the evolution of the type $\Xi_t^i$ is described by pairwise
interactions between different particles under a series of chemical reactions
described by a chemical reaction network. We prove that in the large particle
limit the stochastic dynamics converges to a mean field limit which is
described by a nonlocal reaction-diffusion partial differential equation. In
particular, we obtain a quantitative propagation of chaos result for the
interacting particle system. Our proof is based on the relative entropy method
used recently by Jabin and Wang \cite{JW18}. The key ingredient of the relative
entropy method is a large deviation estimate for a special partition function,
which was proved previously by technical combinatorial estimates. We give a
simple probabilistic proof based on a novel martingale argument.
