Using a large skillet, heat the oil over medium-high heat. Add the chicken, and brown for about 3 minutes per side. Transfer to a plate and set aside.
Add the shallot to the pan, and cook stirring until fragrant, about 1 minute. Add the broth and bring the mixture to a simmer. Using a spatula or wooden spoon, scrape any browned bits from the bottom.
Spread the bulgur over the bottom of a glass or ceramic baking dish. Pour the broth mixture over couscous, add the zest, lemon juice, thyme, season with salt and pepper, and stir to combine. Arrange chicken on top of couscous, and add the tomatoes. Cover the dish tightly with aluminum foil and bake in the oven until the chicken is cooked through and the broth has been absorbed, about 20 minutes (depending on the thickness of the breasts).
Transfer the chicken to a plate. Add the fresh herbs to the bulgur, stir well to combine, then fluff with a fork. Line the serving plates with arugula, mound the bulgur mixture on top along with a chicken breast. Season with salt and pepper, if desired and enjoy!