abstract: The narrow escape problem deals with the calculation of the mean escape time (MET) of a Brownian particle from a bounded domain through a small hole on the domain’s boundary. We developed a formalism which allows one to evaluate the nonescape probability of a gas of diffusing particles that may interact with each other. In some limits we can also evaluate the MET of the first particle. The formalism is based on the fluctuating hydrodynamics and macroscopic fluctuation theory. We also uncover a direct mathematical connection between the narrow escape of interacting particles and thermal runaway in chemical reactors.