Gather all ingredients.
Preheat the oven to 400 degrees F (200 degrees C). Sprinkle chicken thighs evenly with 1/2 teaspoon salt. Heat 1 tablespoon oil in a deep 12-inch skillet over medium-high heat. Add chicken to skillet, skin side down. Cook until skin is browned, 6 to 8 minutes. Turn and brown on the second size, 4 minutes. Remove chicken from skillet.
Add onion to skillet. Cook and stir until tender, 5 minutes. Add garlic. Cook and stir until fragrant, about 1 minute.
Add remaining 2 tablespoons oil to skillet. Add eggplant. Cook and stir until softened, 5 minutes.
Add bell peppers and zucchini to skillet. Cook and stir until vegetables are tender, 10 minutes.
Stir in tomatoes, 3 tablespoons basil, the thyme, rosemary, remaining 3/4 teaspoon salt, and pepper. Bring to a boil and cook, stirring occasionally, until tomatoes start to break down, 8 minutes.
Nestle chicken into the ratatouille mixture, skin side up.
Bake until chicken is done (170 degrees F or 77 degrees C) and ratatouille is bubbling and saucy, 20 minutes. Garnish with remaining 1 tablespoon basil.