Sprinkle chicken with salt and pepper. Heat butter and oil in 12-inch sauté pan over medium-high heat. When butter foaming subsides, add chicken; sauté until browned on both sides, moving around to brown evenly, 10 to 15 minutes. Remove from pan and set aside.
Discard all but thin film of fat from pan. Add onion, carrots, and turnips; sauté, stirring frequently to prevent scorching, until pan juices evaporate, 4 to 5 minutes. Add garlic and sauté until fragrant.
Return chicken and accumulated juices to pan, moving vegetables to top. Add thyme sprigs, spices, chickpeas, and reserved chickpea cooking liquid; bring to boil. Lower heat, cover, and barely simmer until chicken is cooked through, basting three or four times, about 25 minutes. Place portion of chicken on each plate; top with vegetables. Ladle juices over both chicken and vegetables and serve immediately.