Pat chicken dry with paper towels and season with salt and pepper. Heat oil in 10-inch skillet over medium-high heat until just smoking. Brown chicken well, about 5 minutes per side. Transfer chicken to plate, let cool slightly, then remove skin.

Pour off all but 1 tablespoon fat from skillet. Add potatoes, carrots, onion, and ¼ teaspoon salt and cook over medium heat until onion is softened, about 5 minutes. Stir in garlic and thyme and cook until fragrant, about 30 seconds. Stir in broth and wine, scraping up any browned bits.

Nestle browned chicken into vegetables, add any accumulated juices, and bring to a simmer. Reduce heat to medium-low, cover, and simmer until chicken is very tender and almost falling off bone, about 1 hour, flipping chicken halfway through cooking. Transfer chicken to serving dish and tent loosely with aluminum foil.

Increase heat to medium, stir in fennel and cinnamon, simmer uncovered until vegetables are tender and sauce is slightly thickened, about 8 minutes. Stir in any chicken juices and simmer for 30 seconds. Off heat, stir in lemon juice and season with salt and pepper. Spoon vegetables and sauce over chicken and serve.