The article under review studies a large deviation principle for an interacting particle system associated with a nonlinear and nonlocal reaction-diffusion equation. More precisely, let $\{X_i, i\geq 1\}$ be an i.i.d.\ sequence of exponential random variables of rate 1 and $\{B_i, i\geq 1\}$ be a collection of independent $d$-dimensional Brownian motions, independent of $\{X_i, i\geq 1\}$. Given a continuous function $\zeta\:\Bbb{R}^d\to\Bbb{R}_+$ with sub-quadratic growth let us define $$ \mu^n(t)=\frac{1}{n}\sum_{i=1}^n \delta_{B_i(t)} \,\bold 1_{\{X_i> \int_0^t \langle \zeta, \mu^n(s)\rangle ds\}}. $$ It is shown in Theorem 2.1 that $\mu^n\to\mu$, as $n\to\infty$, in probability where $\mu(t)$ has a density $u(t, \cdot)$ satisfying $$ \partial_t u(t, x)=\frac{1}{2}\Delta u(t, x) - \langle \zeta, u\rangle \, u(t, x) \quad \text{in}\; (0, \infty)\times \Bbb{R}^d,\quad \text{and}\quad \lim_{t\to 0} u(t, \cdot)=\delta_0. $$ The main result (Theorem 3.1) of this article establishes a large deviation principle of the sub-probability measures $\{\mu^n, n\geq 1\}$.