A reaction - diffusion equation is studied with linear dynamics in the medium and a nonlinear boundary condition. The diffusion occurs in a domain that is perforated by periodically placed holes. On the boundary of these holes, the nonlinear boundary condition is applied. Wavefront propagation is established by use of a Feynman - Kac representation of the solution and development of an appropriate large deviations principle. The location of the wavefront is described in terms of the Legendre transform of the solution to an eigenvalue problem. The proof uses periodicity in an essential way by application of Doeblin's condition to the associated random process on the torus.