The one-dimensional free Fermi gas is a prototype conformally invariant system whose entanglement properties are well understood. In this paper, the effects of a single impurity on one-dimensional free fermion entanglement entropy are studied both analytically and numerically. Such an impurity represents an exactly marginal perturbation to the bulk conformally invariant fixed point. We find that the impurity leads to subleading contributions to the entanglement entropy that scale inversely with the subsystem size. The origins of such contributions are identified.