In a large, heavy, flameproof casserole, cook the onions and leeks in the olive oil over moderate heat until soft but not brown, 4 to 5 minutes. Stir in the garlic and tomatoes. Cover and cook until the tomatoes begin to exude their juices, about, 5 minutes. Uncover and boil over moderately high heat, stirring frequently, until the mixture is almost dry, 4 to 5 minutes. Season the chicken with salt and pepper and arrange the pieces in the casserole, spreading the vegetables over and around them. Cover and cook for 5 minutes, then turn the chicken and cook for 5 minutes longer. Pour in the stock and wine, adding just enough liquid barely to cover the chicken. Add the bay leaves, thyme, fennel seeds, saffron, orange peel and hot pepper sauce. Season lightly with salt and pepper. Cover and simmer for 15 to 25 minutes, depending on the cuts youve selected. The chicken is done when the meat feels just springy at the fleshiest part and the juices run clear yellow if the meat is pierced. Transfer the chicken to a plate. Remove the skin. Tip the casserole and skim the fat from the cooking juices. Return the chicken to the casserole. (The stew can be made to this point up to 1 day ahead. Refrigerate it uncovered, then cover when chilled.) Make the aioli: Puree the garlic cloves in a mortar. Add 1/2 teaspoon salt and pound to a fine paste. Pound in the bread crumbs and a few drops of the vinegar. Add the egg yolks and pound to a thick and sticky mass. Whisk in the oil by droplets to make a thick sauce. If the aioli becomes very stiff, whisk in drops of vinegar. Season with salt. If not serving shortly, cover with plastic wrap and refrigerate. Bring the stew just to a simmer. Gradually and by dribbles, whisk 1 cup of the hot cooking liquid into the aioli. Pour the aioli into the casserole and swirl slowly over moderate heat for several minutes until the sauce thickens to the consistency of light cream. Be very careful not to let the sauce come near a simmer (the yolks will scramble), but you must let it heat to the point of thickening; it will register over 160°, enough to kill off any harmful bacteria! Discard the bay leaves. Ladle the stew into warm soup plates. Add a serving of potatoes and garnish with the parsley. Serve immediately, with a fork, knife and spoon. NOTES : Bourride is a lively intensely garlicky fish stew from Provence. Its unique flavor comes from a final enrichment with aioli, the famous Mediterranean garlic mayonnaise. Marvelous with fish, this stew is equally delicious when made with chicken, and its time to give those birds something new to think about. To make bourride, you start out with the familiar robust base of onions, leeks, garlic and tomatoes cooked in olive oil. Then the chicken is put in, followed by wine, stock, herbs and seasoning. The final touch is blending in the aioli.