In a large skillet, heat the remaining 3 tablespoons of olive oil. Add the shallots and the remaining anchovy fillet and cook over moderate heat, stirring occasionally, until the shallots are softened, about 5 minutes. Add the snap peas and cook, tossing a few times, until heated through, about 2 minutes. Season the snap peas with salt and transfer to a serving bowl. Serve the chicken with the snap peas.