The decay of metastable states in spatially one-dimensional systems by kink nucleation at the sample boundaries is investigated for a specific bistable reaction-diffusion system. An expression for the nucleation rate is derived in the framework of multidimensional Kramers theory, and the dependence of the rate on the boundary conditions is discussed. It turns out that the question whether homogeneous kink nucleation in the bulk or heterogeneous kink nucleation at the sample boundary predominates depends on the specific type of the boundary.