Preheat oven to 425°F. Season chicken with 1 teaspoon salt and ½ teaspoon pepper. Heat oil in a large ovenproof skillet over high heat until hot but not smoking. Brown chicken on all sides, 8 to 10 minutes. Transfer to a plate.
Pour off all but 1 tablespoon fat. Reduce heat to medium-high. Brown fennel wedges, artichokes, and onion in skillet, stirring occasionally, 2 to 3 minutes.
Return chicken to skillet. Add stock. Transfer to oven. Braise until cooked through, 18 to 20 minutes.
Transfer chicken and vegetables to a platter. Reduce braising liquid over high heat to about ⅓ cup. Stir in vinegar. Pour sauce over chicken, and top with fennel fronds and parsley.
