Preheat the oven to 400°F.
Set a large Dutch oven over medium-high heat. Add 1/2 tablespoon olive oil and heat to shimmering.
Pat the chicken dry with paper towels, season on all sides with salt and pepper, and set the chicken down in the pan. Cook, without moving, until nicely browned and the meat releases from the pan, about 5 minutes.
Flip and continue cooking until the other side begins to brown, about 3 minutes. Remove the chicken to a plate and set aside.
Reduce the heat to medium and add the remaining olive oil, onion, garlic, and a pinch of salt. Cook, stirring occasionally, until the vegetables begin to soften, about 3 minutes.
Add the eggplant and another pinch of salt and cook, stirring occasionally, until the eggplant begins to soften, about 5 minutes.
Add the tomato paste and thyme and cook, stirring constantly, for 1 minute.
Add the zucchini, bell pepper, tomatoes, another pinch of salt, and a twist of black pepper and cook, stirring occasionally, until all of the vegetables are tender, about 10 minutes.
Remove the pan from the heat.
Partially submerge the chicken into the vegetables. Transfer the pot to the oven and cook, uncovered, until the thickest portion of the chicken reaches an internal temperature of 160°F, about 20 minutes.
Remove from the oven and let stand for 10 minutes. Stir in the basil and serve.