In a large skillet, heat 2 tablespoons olive oil over medium heat. Season the chicken with salt and pepper, add to the pan and cook, turning once, until cooked through, about 10 minutes. Transfer to a work surface, let cool, then shred; reserve the skillet.
Meanwhile, in a large saucepan, bring 2 cups chicken broth and 1 tablespoon olive oil to a boil; season with salt and pepper. Add the couscous, cover and remove from the heat; let stand for 5 minutes, then fluff with a fork.
In the reserved skillet, heat the remaining 1 tablespoon olive oil over medium heat. Add the onion and cook until softened, about 5 minutes. Add the broccoli and the remaining 1 cup chicken broth and simmer for 5 minutes. Stir in the chicken, raisins, parsley and couscous; season with salt and pepper. Toss with the almonds before serving.