Preheat the oven to 350 degrees.
Heat 3 tablespoons of olive oil in a medium (11-inch) Dutch oven, such as Le Creuset, over medium to medium-high heat. Dry the chicken all over, place it in the pot breast side down, and sear it for 5 to 7 minutes without moving, until the skin is nicely browned. Turn the chicken breast side up and sear for another 4 to 5 minutes, until browned on the bottom. Transfer the chicken to a plate.
Add the carrots, celery, leeks, and fennel to the pot and sauté for 10 to 15 minutes, stirring occasionally, until the vegetables start to brown. Add the garlic and cook for one minute. Return the chicken to the pot, breast side up, spreading the vegetables around the chicken. Add the chicken stock, saffron, and enough water to cover the chicken with just an inch of the breastbone exposed. Tie the thyme, parsley, and dill together in a bundle with kitchen string and add to the pot along with 1½ tablespoons salt and 1½ teaspoons pepper. Bring to a boil, cover, and bake for 1 hour and 15 minutes, checking to be sure the liquid is simmering.
Discard the herb bundle, stir the orzo into the broth, cover, and allow to sit off the heat for 20 to 25 minutes, until the orzo is tender. Using forks to separate the chicken into quarters, carefully pull the breast meat away from the bones (I leave the bones in the leg portion) and reheat, if necessary. Spoon some of the chicken, broth, and pasta into large shallow bowls, and serve hot sprinkled generously with minced dill and salt.
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