In a large, deep skillet, heat 2 tablespoons olive oil over medium heat. Add the chicken and cook, turning occasionally with tongs, until golden-brown, 6 to 8 minutes. Transfer to a plate and set aside.
In the same skillet, add the onion and cook over medium heat, stirring, until softened, about 3 minutes. Add the garlic and stir for about 1 minute. Pour in the chicken broth and scrape up any browned bits from the bottom of the pan. Return the chicken to the pan and add the lemons, olives and thyme. Season lightly with salt and pepper. Bring to a simmer, cover and cook over low heat until the chicken is falling off the bone, about 50 minutes.
About 10 minutes before the chicken is done, in a small, heavy saucepan, bring 1 1/4 cups water to a boil. Sir in the remaining 1 tablespoon olive oil and the couscous; remove from the heat, cover and let stand for 3 minutes. Divide the couscous among 4 plates and top with 2 to 3 chicken pieces and some sauce.