Put the oil in a large deep skillet, preferably nonstick, and turn the heat to medium. A minute later, add the chicken pieces, skin side down, and brown well, seasoning with salt and pepper and adjusting the heat and rotating the pieces so they brown evenly, about 10 minutes. When they are done, transfer them to a plate.
Add the garlic and anchovies if you’re using them and cook, stirring occasionally, until the garlic begins to take on some color, about 5 minutes. Add the onions and the bell pepper and cook, stirring occasionally, until they soften, about 10 minutes. Add the saffron, herb, and capers and stir, then add the tomatoes and olives. Stir, bring to a boil, and return the chicken, skin side up, to the skillet.
Cover and cook over medium-low heat—the mixture should bubble, but gently—until the chicken is done, 20 to 30 minutes. Garnish and serve.
