Step 1To prepare the artichokes, fill a large bowl with a couple of quarts of cold water, and squeeze in the juice of a medium lemon (drop in the cut lemon halves too). Trim the artichokes one at a time, first snapping off the thick outside leaves, until you reach the tender, pale inner leaves. Trim the tip of the stem, but leave most of it attached to the base of the artichoke. With a sharp paring knife or vegetable peeler, shave off the dark skin of the stem, exposing the tender core. Peel around the globe of the artichoke too, removing the dark-green spots where the tough leaves were attached. Cut across the leaf tips with a serrated knife, removing the top third of the artichoke. Slice the entire artichoke in half lengthwise, splitting the bulb and stem and drop the pieces into the acidulated water.
Step 2Rinse the chicken, and pat it dry. Cut it into 10 or 12 pieces (including the backbone), and season with one-half teaspoon salt.
Step 3In a large saucepan, heat the olive oil over medium-high heat, and lay the chicken pieces in it without crowding -- cook them in batches if necessary. Brown the pieces for about 3 minutes on each side, until each is nicely colored on all sides. Remove the pieces to a platter or bowl.
Step 4When all the chicken is out of the pan, drop the crushed garlic into the hot fat and cook for a minute or two, until sizzling. Lift the artichokes out of the water, and drop them, still damp, into the saucepan. Stir well, and season them with one-half teaspoon salt and the peperoncino flakes.
Step 5Cook the artichokes for 4 or 5 minutes, tossing them often and deglazing the browned bits in the pan bottom. When the artichokes are dry and starting to take color, carefully pour in the wine and cook over high heat, stirring, until it is nearly evaporated, about 3 minutes longer.
Step 6Pour in the tomatoes with their juices and 3 cups water; slosh the tomato container with some of the water to rinse the remaining juices into the pan. Cover the pan, and bring the liquid to a boil. Adjust the heat to maintain a steady bubbling, and cook the artichokes and sauce for about 15 minutes.
Step 7Return all the chicken pieces (and any accumulated juices on the platter) to the saucepan, submerging them in the sauce. Cover the pan and cook the chicken and artichokes together for about 40 minutes, after which the chicken should be nearly done, the artichokes tender and the sauce somewhat reduced. Set the cover ajar -- or remove it altogether -- and continue cooking 15 to 25 minutes or more, until the sauce has thickened and coats the chicken and artichoke pieces. Taste and adjust the seasoning.
Step 8Serve immediately, or, for best flavor, let the chicken cool in the pot and reheat later. If the sauce has thickened, stir in a bit of water. Serve hot from the pan, or from a big bowl. Sprinkle the parsley over it just before serving.