1. Preheat oven to 375°. Heat oil in a 12-in. ovenproof frying pan over medium-high heat. Generously sprinkle both sides of chicken with 1/4 tsp. each salt and pepper, then carefully lay meat skin side down in hot oil. Add potatoes to pan around chicken pieces. Cook, covered and shaking pan often, until chicken is golden brown and skin is crispy, about 7 minutes.
2. Using tongs, turn chicken over and stir any browned potatoes. Sprinkle chicken and potatoes with thyme and lemon zest. Lay broccoli evenly over chicken and potatoes; sprinkle with remaining 1/4 tsp. each salt and pepper.
3. Put uncovered pan in oven. Cook until potatoes are tender when pierced, stirring once, 15 to 20 minutes.
Note: Nutritional analysis is per serving.